// Start COMPLEX NUMBERS
// Start COMPLEX NUMBERS
// Start EQUALITY ETC
// Start FUNCTIONS
// Start NUMBER THEORY
// Start NUMBER SETS
// Start MATRICES
// Start POLYNOMIALS
//Start SETS
// Start SYSTEMS OF EQUATIONS AND INEQUALITIES
// Start SEQUENCES
//Start Geometric Figures
var def_line=
'A line is a straight set of points that extends into infinity in both directions.';
var def_square=
'A square is a quadrilateral with four equal sides and four 90 degree angles.';
var def_parallelogram=
'A parallelogram is a quadrilateral with opposite sides parallel.';
var def_rectangle=
'A rectangle is a quadrilateral with four 90-degree angles.';
var def_triangle=
'A triangle is a three-sided polygon.';
var def_trapezoid=
'A trapezoid is a quadrilateral that has exactly two sides parallel.';
var def_circle =
'A circle is the set of points in a plane that are '
+'equidistant from a fixed point called the center.';
var def_radius =
'The radius of a circle is the fixed distance from the '
+'center of the circle to any point on the circle.';
var def_annulus =
'An annulus is the area between two coplanar concentric circles.';
var def_polygon=
'';
var def_quadrilateral=
'A quadrilateral is a four sided polygon.';
var def_triangle=
'A triangle is a three sided polygon.';
var def_right_triangle=
'A right triangle is a triangle that contains a right angle.';
var def_sphere=
'A sphere is a three-dimensional figure with all points in space a fixed distance from a given point, '
+'called the center.';
var def_cylinder=
'A cylinder is a three-dimensional figure having two parallel '
+'bases that are congruent circles.';
var def_cone=
'A cone is A three-dimensional figure with one vertex and a circular base.';
// Start MISCELLANEOUS NOTATION ETC.
var def_factorial =
'If n is a natural number, n factorial '
+'is the product of all positive integers less than or equal to n. '
+'The factorial of n is denoted by n! and may be defined/computed with the following '
+'formula.
n! = (1)(2)(3) ... (n - 1)(n).';
var def_summation_notation =
'The nth partial sum (the sum of the first n terms) of a sequence named a is represented by
'
+'
'
+'
where i is the index of summation, 1 is the lower limit, and n is the upper limit.';
// Start SEQUENCES
var def_sequence =
'A sequence is a function whose domain is the set of '
+'Natural Numbers.';
var def_partial_sum =
'The nth partial sum of a sequence is defined to be the '
+'sum of the first n terms of the sequence.';
// Start COMPLEX NUMBERS
var def_complex_numbera_keyword =
'
'
+'Complex Number';
var def_complex_numbera_caption =
'Definition
Complex Number';
var def_complex_numbera =
' A complex number is a number that can be written in the form a + bi where a and b are '
+'real numbers and '
+'
.';
var def_real_component_keyword =
'
'
+'Real Component';
var def_real_component_caption =
'Definition
Real Component';
var def_real_component =
' The real component of the complex number a + bi is a.';
var def_complex_component_keyword =
'
'
+'Complex Component';
var def_complex_component_caption =
'Definition
Complex Component';
var def_complex_component =
' The complex component of the complex number a + bi is b.';
var def_sum_of_complex_numbers_keyword =
'
'
+'Sum of Complex Numbers';
var def_sum_of_complex_numbers_caption =
'Definition
Sum of Complex Numbers';
var def_sum_of_complex_numbers =
' The sum of two complex numbers a + bi and c + di is defined by (a + bi) + (c + di) = (a + c) + (b + d)i.';
var def_opposite_of_complex_number_keyword =
'
'
+'Opposite of a Complex Number';
var def_opposite_of_complex_number_caption =
'Definition
Opposite of a Complex Number';
var def_opposite_of_complex_number =
' The opposite of a complex number a + bi is -a - bi.';
var def_difference_of_complex_numbers_keyword =
'
'
+'Difference of Complex Numbers';
var def_difference_of_complex_numbers_caption =
'Definition
Difference of Complex Numbers';
var def_difference_of_complex_numbers =
' The difference (a + bi) - (c + di) is defined to be (a + bi) + (-c - di).';
var def_product_of_complex_numbers_keyword =
'
'
+'Product of Complex Numbers';
var def_product_of_complex_numbers_caption =
'Definition
Product of Complex Numbers';
var def_product_of_complex_numbers =
' The product (a + bi)(c + di) is defined to be (ac - bd) + (bc + ad)i.';
var def_norm_of_complex_number_keyword =
'
'
+'Norm of a Complex Number';
var def_norm_of_complex_number_caption =
'Definition
Norm of a Complex Number';
var def_norm_of_complex_number =
' The norm of a complex number a + bi is a2 + b2.';
var def_conjugate_of_complex_number_keyword =
'
'
+'Conjugate of a Complex Number';
var def_conjugate_of_complex_number_caption =
'Definition
Conjugate of a Complex Number';
var def_conjugate_of_complex_number =
' The conjugate of a complex number a + bi is a - bi.';
var def_inverse_of_complex_number_keyword =
'
'
+'Inverse of a Complex Number';
var def_inverse_of_complex_number_caption =
'Definition
Inverse of a Complex Number';
var def_inverse_of_complex_number =
' The multiplicative inverse of a complex number a + bi is its conjugate divided by '
+'its norm '
+'
.';
var def_quotient_of_complex_number_by_a_real_keyword =
'
'
+'Quotient of a Complex Number by a Real Number';
var def_quotient_of_complex_number_by_a_real_caption =
'Definition
Quotient of a Complex Number by a Real Number';
var def_quotient_of_complex_number_by_a_real =
' The quotient of a complex number by a real number is the
'
+'complex number multiplied by the reciprocal of the divisor. ';
var def_quotient_of_complex_numbers_keyword =
'
'
+'Quotient of Complex Numbers';
var def_quotient_of_complex_numbers_caption =
'Definition
Quotient of Complex Numbers';
var def_quotient_of_complex_numbers =
' The quotient 
is defined to be '
+'
';
// Start EQUALITY ETC
var def_operand=
'An operand is a mathematical object upon which an operator acts.';
var def_unary_operation =
'A unary operation is a calculation involving one operand.';
var def_binary_operation =
'A binary operation is a calculation involving two operands.';
var def_binary_relation =
'A binary relation is a comparison of two operands.';
var def_inequality =
'An inequality is a mathematical statement which contains an inequality symbol.';
var def_equality_of_real_numbers =
'Two real numbers a and b are equal if they represent the same point on the number line.
'
+'The symbol = written between two numbers is used to indicate the two numbers are related by equality.';
var def_less_than =
'The real number a is less than b if a is to the left of b on the number line.
'
+'The symbol < written between two numbers is used to indicate the two numbers are related by less than.';
var def_greater_than =
'The real number a is greater than b if a is to the right of b on the number line.
'
+'The symbol > written between two numbers is used to indicate the two numbers are related by greater than.';
var def_less_than_or_equal =
'The real number a is less than or equal to b if a is less than b or equal to b.
'
+'The symbol ≤ written between two numbers is used to indicate the two numbers are related by less than or equal to.';
var def_greater_than_or_equal =
'The real number a is greater than or equal to b if a is greater than b or equal to b.
'
+'The symbol ≥ written between two numbers is used to indicate the two numbers are related by greater than or equal to.';
var def_equality_of_complex_numbers_keyword =
'
'
+'Equality of Complex Numbers';
var def_equality_of_complex_numbers_caption =
'Definition
Equality of Complex Numbers';
var def_equality_of_complex_numbers =
'Two complex numbers a + bi and c + di are equal if a = c and b = d.';
var def_equality_of_sets_keyword =
'
'
+'Equality of Sets';
var def_equality_of_sets_caption =
'Definition
Equality of Sets';
var def_equality_of_sets =
'Two sets are equal if they contain exactly the same elements.
'
+'Symbolic Form: 
';
var def_equality_of_ordered_pairs_keyword =
'
'
+'Equality of Ordered Pairs';
var def_equality_of_ordered_pairs_caption =
'Definition
Equality of Ordered Pairs';
var def_equality_of_ordered_pairs =
'Two ordered pairs (a, b) and (c, d)equal if
a = c and b = d.';
var def_equality_of_ordered_triples_keyword =
'
'
+'Equality of Ordered Triples';
var def_equality_of_ordered_triples_caption =
'Definition
Equality of Ordered Triples';
var def_equality_of_ordered_triples =
'Two ordered triples (a, b, c) and (d, e, f) are equal if a = d, b = e, and c = f.';
var def_equality_of_polynomials_keyword =
'
'
+'Equality of Polynomials';
var def_equality_of_polynomials_caption =
'Definition
Equality of Polynomials';
var def_equality_of_polynomials =
'Two polynomials are equal if they have the same degree and corresponding coefficients are equal.';
var def_equality_of_functions_keyword =
'
'
+'Equality of Functions';
var def_equality_of_functions_caption =
'Definition
Equality of Functions';
var def_equality_of_functions =
'Two functions f and g are equal if they have the same domains, the same ranges, and f(x) = g(x) '
+'for every x in the common domain.';
// Start FUNCTIONS
var def_function_keyword =
'
'
+'Function';
var def_function_caption =
'Definition
Function';
var def_function =
' A function consists of three things:
'
+'A set called the Domain
'
+'A set called the Range
'
+'A rule which associates each element of the domain with a unique element of the range.';
var def_functional_notation_keyword =
'
'
+'Functional Notation';
var def_functional_notation_caption =
'Definition
Functional Notation';
var def_functional_notation =
' 
';
var def_sum_of_functions_keyword =
'
'
+'Sum of Functions';
var def_sum_of_functions_caption =
'Definition
Sum of Functions';
var def_sum_of_functions =
' The sum of two functions f and g with the same domain is the function named (f+g) whose rule may be written as
'
+' (f+g)(x) = f(x) + g(x) for all x in the common domain.';
var def_product_of_functions_keyword =
'
'
+'Product of Functions';
var def_product_of_functions_caption =
'Definition
Product of Functions';
var def_product_of_functions =
' The product of two functions f and g with the same domain is the function named (fg) whose rule may be written as
'
+' (fg)(x) = [f(x)][g(x)] for all x in the common domain.';
var def_difference_of_functions_keyword =
'
'
+'Difference of Functions';
var def_difference_of_functions_caption =
'Definition
Difference of Functions';
var def_difference_of_functions =
' The difference of two functions f and g with the same domain is the function named (f-g) whose rule may be written as
'
+' (f-g)(x) = f(x) - g(x) for all x in the common domain.';
var def_quotient_of_functions_keyword =
'
'
+'Quotient of Functions';
var def_quotient_of_functions_caption =
'Definition
Quotient of Functions';
var def_quotient_of_functions =
' The quotient of two functions f and g with the same domain is the function named '
+'
'
+'whose rule may be written as
'
+'
'
+'for all x in the common domain.';
var def_composition_of_functions_keyword =
'
'
+'Composition of Functions';
var def_composition_of_functions_caption =
'Definition
Composition of Functions';
var def_composition_of_functions =
' The composition of a function f with a function g is a function named '
+'
whose rule is
'
+' 
.
'
+'The domain of '
+'is the set of all x in the domain of g for which g(x) is in the domain of f.';
var def_inverse_of_a_function_keyword =
'
'
+'Inverse of a Function';
var def_inverse_of_a_function_caption =
'Definition
Inverse of a Function';
var def_inverse_of_a_function =
' Let f be a function with domain A and range B. Then the inverse of the function, if it exists, '
+'is a function named f-1, '
+'with domain B and range A with the property that
'
+'
';
var def_graph_of_a_function =
' The graph of a function is the set of all points whose coordinates satisfy the rule '
+'of the function.';
var def_graph_of_a_function_alternate_keyword =
'
'
+'Graph of a Function';
var def_graph_of_a_function_alternate_caption =
'Definition
Graph of a Function';
var def_graph_of_a_function_alternate =
' The graph of a function is the set of all points of the form (a, f(a))
'
+' where a is an element of the domain and f(a) is the corresponding range element.';
var def_increasing_function_keyword =
'
'
+'Increasing Function';
var def_increasing_function_caption =
'Definition
Increasing Function';
var def_increasing_function =
' A function f is increasing on an interval if, for any x1and x2 in the interval, '
+'
x1< x2 implies f(x1) < f(x2).';
var def_decreasing_function_keyword =
'
'
+'Decreasing Function';
var def_decreasing_function_caption =
'Definition
Decreasing Function';
var def_decreasing_function =
' A function f is decreasing on an interval if, for any x1and x2 in the interval, '
+'
x1< x2 implies f(x1) > f(x2).';
var def_constant_function_keyword =
'
'
+'Constant Function';
var def_constant_function_caption =
'Definition
Constant Function';
var def_constant_function =
' A function f is called a constant function if its rule can be written as '
+' f(x) = k for some real number k. ';
var def_even_function_keyword =
'
'
+'Even Function';
var def_even_function_caption =
'Definition
Even Function';
var def_even_function =
' A function f is an even function if, f(x) = f(-x) for all domain elements x';
var def_odd_function_keyword =
'
'
+'Odd Function';
var def_odd_function_caption =
'Definition
Odd Function';
var def_odd_function =
' A function f is an odd function if, f(x) = -f(-x) for all domain elements x';
var def_one_to_one_function_keyword =
'
'
+'One to One Function';
var def_one_to_one_function_caption =
'Definition
One to One Function';
var def_one_to_one_function =
' A function is called a one-to-one function if no element of the range is the '
+'associate of more than one domain element.';
var def_zero_of_a_function_keyword =
'
'
+'Zero of a Function';
var def_zero_of_a_function_caption =
'Definition
Zero of a Function';
var def_zero_of_a_function =
' A zero of a function f is a domain element k
for which f(k) = 0.';
var def_rule_of_a_function =
' A rule which associates each element of the domain with a unique element of the range.';
var def_satisfy_the_rule =
' The coordinates of a point (a, b) are said to satisfy the rule of a function f if b = f(a).';
var def_zero_function_keyword =
'
'
+'Zero Function';
var def_zero_function_caption =
'Definition
Zero Function';
var def_zero_function =
'The zero function z is the function defined by z(x) = 0 for all x in the domain of z.';
var def_identity_function_keyword =
'
'
+'Identity Function';
var def_identity_function_caption =
'Definition
Identity Function';
var def_identity_function =
'The identity function is the function I which has the property that I(x) = x for '
+'all x in the domain of I.';
var def_absolute_value_function_keyword =
'
'
+'Absolute Value Function';
var def_absolute_value_function_caption =
'Definition
Absolute Value Function';
var def_absolute_value_function =
'The absolute value function is a function abs whose rule may be written in the '
+'form abs(x) = | x |.';
var def_squaring_function_keyword =
'
'
+'Squaring Function';
var def_squaring_function_caption =
'Definition
Squaring Function';
var def_squaring_function =
'The squaring function is the quadratic function f whose rule may be written '
+'in the form f(x) = x2.';
var def_cubing_function_keyword =
'
'
+'Cubing Function';
var def_cubing_function_caption =
'Definition
Cubing Function';
var def_cubing_function =
'The cubing function is the function f whose rule may be written '
+'in the form f(x) = x3.';
var def_reciprocal_function_keyword =
'
'
+'Reciprocal Function';
var def_reciprocal_function_caption =
'Definition
Reciprocal Function';
var def_reciprocal_function =
'The reciprocal function is the function f whose rule may be written '
+'in the form 
.';
var def_square_root_function_keyword =
'
'
+'Square Root Function';
var def_square_root_function_caption =
'Definition
Square Root Function';
var def_square_root_function =
'The square root function is the function sqrt whose rule may be written '
+'in the form 
.';
var def_cube_root_function_keyword =
'
'
+'Cube Root Function';
var def_cube_root_function_caption =
'Definition
Cube Root Function';
var def_cube_root_function =
'The cube root function is the function f whose rule may be written '
+'in the form 
.';
var def_greatest_integer_function_keyword =
'
'
+'Greatest Integer Function';
var def_greatest_integer_function_caption =
'Definition
Greatest Integer Function';
var def_greatest_integer_function =
'The greatest integer function is the function int whose rule may be written '
+'in the form 
, '
+' where 
means the '
+'greatest integer less than or equal to x';
var def_piecewise_defined_function_keyword =
'
'
+'Piecewise Defined Function';
var def_piecewise_defined_function_caption =
'Definition
Piecewise Defined Function';
var def_piecewise_defined_function =
'A piecewise defined function is a function whose rule is different for different '
+'intervals of its domain.';
var def_linear_function_keyword =
'
'
+'Linear Function';
var def_linear_function_caption =
'Definition
Linear Function';
var def_linear_function =
'A linear function is a function whose rule may be written in the form f(x) = mx + b'
+' where m and b are real numbers.';
var def_quadratic_function_keyword =
'
'
+'Quadratic Function';
var def_quadratic_function_caption =
'Definition
Quadratic Function';
var def_quadratic_function =
'A quadratic function is a function whose rule may be written in the form f(x) = ax2 + bx + c'
+' where a, b, and c are real numbers and a is not zero.';
var def_polynomial_function_keyword =
'
'
+'Polynomial Function';
var def_polynomial_function_caption =
'Definition
Polynomial Function';
var def_polynomial_function =
'A polynomial function is a function whose rule may be written'
+' in the form '
+'f(x) = anxn + an-1xn-1 + ... + a1'
+'x + a0
'
+' where an, an-1, ... a1 and '
+'a0 are all real numbers '
+'and n is a whole number.';
var def_rational_function_keyword =
'
'
+'Rational Function';
var def_rational_function_caption =
'Definition
Rational Function';
var def_rational_function =
'A rational function is a function whose rule may be written in the form
'
+'
'
+' where N and D are polynomial functions';
var def_exponential_base_a_function_keyword =
'
'
+'Exponential base a Function';
var def_exponential_base_a_function_caption =
'Definition
Exponential base a Function';
var def_exponential_base_a_function =
'The Exponential base a Function is the function expa whose rule may be written in the form
'
+'expa(x) = ax
where a is any positive real number other than 1.';
var def_exponential_base_e_function_keyword =
'
'
+'Exponential base e Function';
var def_exponential_base_e_function_caption =
'Definition
Exponential base e Function';
var def_exponential_base_e_function =
'The Exponential base e Function is the function exp whose rule may be written in the form
'
+'exp(x) = ex
where e is the irrational number approximately equal to 2.718281828...';
var def_exponential_base_2_function_keyword =
'
'
+'Exponential base 2 Function';
var def_exponential_base_2_function_caption =
'Definition
Exponential base 2 Function';
var def_exponential_base_2_function =
'The Exponential base 2 Function is the function exp2 whose rule may be written in the form
'
+'exp2(x) = 2x.';
var def_exponential_base_10_function_keyword =
'
'
+'Exponential base 10 Function';
var def_exponential_base_10_function_caption =
'Definition
Exponential base 10 Function';
var def_exponential_base_10_function =
'The Exponential base 10 Function is the function exp10 whose rule may be written in the form
'
+'exp10(x) = 10x.';
var def_logarithm_base_e_function_keyword =
'
'
+'Logarithm base e Function';
var def_logarithm_base_e_function_caption =
'Definition
Logarithm base e Function';
var def_logarithm_base_e_function =
'The Logarithm base e Function is the function ln which is the inverse of the function exp.';
var def_logarithm_base_2_function_keyword =
'
'
+'Logarithm base 2 Function';
var def_logarithm_base_2_function_caption =
'Definition
Logarithm base 2 Function';
var def_logarithm_base_2_function =
'The Logarithm base 2 Function is the function log2 which is the inverse '
+'of the function exp2.';
var def_logarithm_base_10_function_keyword =
'
'
+'Logarithm base 10 Function';
var def_logarithm_base_10_function_caption =
'Definition
Logarithm base 10 Function';
var def_logarithm_base_10_function =
'The Logarithm base 10 Function is the function log which is the inverse '
+'of the function exp10.';
var def_logarithm_base_a_function_keyword =
'
'
+'Logarithm base a Function';
var def_logarithm_base_a_function_caption =
'Definition
Logarithm base a Function';
var def_logarithm_base_a_function =
'The Logarithm base a Function is the function loga which is the inverse '
+'of the function expa.';
//Start NUMBER THEORY
var def_prime_factorization_keyword =
'
'
+'Prime Factorization';
var def_prime_factorization_caption =
'Definition
Prime Factorization';
var def_prime_factorization =
'If an integer is written as a product of prime numbers, that indicated product is called the '
+'prime factorization of the number.';
//Start NUMBER SETS
var def_natural_number_keyword =
'
'
+'Natural Numbers';
var def_natural_number_caption =
'Definition
Natural Numbers';
var def_natural_number =
'The set of Natural Numbers consists of the common counting numbers.'
+'
Standard Symbol: N'
+'
Symbolic Form: N = {1, 2, 3, 4, … }';
var def_whole_number_keyword =
'
'
+'Whole Numbers';
var def_whole_number_caption =
'Definition
Whole Numbers';
var def_whole_number =
'The set of Whole Numbers consists of the set of Natural Numbers with the number 0 adjoined.'
+'
Standard Symbol: W'
+'
Symbolic Form: W = {0, 1, 2, 3, 4, …} ';
var def_integer_keyword =
'
'
+'Integers';
var def_integer_caption =
'Definition
Integers';
var def_integer =
'The set of Integers consists of the Whole Numbers with their opposites adjoined.'
+'
Standard Symbol: Z'
+'
Symbolic Form: Form: Z = {…, -3, -2, -1, 0, 1, 2, 3, 4, …} ';
var def_rational_number_keyword =
'
'
+'Rational Numbers';
var def_rational_number_caption =
'Definition
Rational Numbers';
var def_rational_number =
'The set of Rational Numbers consists of all numbers which can be written as fractions.'
+'
Standard Symbol: Q'
+'
Symbolic Form: 
';
var def_irrational_number_keyword =
'
'
+'Irrational Numbers';
var def_irrational_number_caption =
'Definition
Irrational Numbers';
var def_irrational_number =
'The set of Irrational Numbers consists of all numbers which cannot be written as fractions.'
+'
Standard Symbol: F.';
var def_real_number_keyword =
'
'
+'Real Numbers';
var def_real_number_caption =
'Definition
Real Numbers';
var def_real_number =
'The set of Real Numbers consists of the set of Rational Numbers with the set of Irrational Numbers adjoined.'
+'
Standard Symbol: R';
var def_complex_number_keyword =
'
'
+'Complex Number';
var def_complex_number_caption =
'Definition
Complex Number';
var def_complex_number =
'A complex number is a number which can be written in the form a + bi where a and b are real numbers and '
+'i is the square root of -1.'
+'
Standard Symbol: C'
+'
Symbolic Form: 
';
var def_prime_number_keyword =
'
'
+'Prime Number';
var def_prime_number_caption =
'Definition
Prime Number';
var def_prime_number =
'A prime number is a natural number greater than 1 which has only 1 and itself as factors.'
+'
Not Standard but Common Symbol: P';
var def_composite_number_keyword =
'
'
+'Composite Number';
var def_composite_number_caption =
'Definition
Composite Number';
var def_composite_number =
'A composite number is a natural number greater than 1 which has more factors than 1 and itself.';
var def_positive_number_keyword =
'
'
+'Positive Number';
var def_positive_number_caption =
'Definition
Positive Number';
var def_positive_number =
'A positive number is a real number greater than 0.';
var def_negative_number_keyword =
'
'
+'Negative Number';
var def_negative_number_caption =
'Definition
Negative Number';
var def_negative_number =
'A negative number is a real number less than 0.';
var def_perfect_square =
'A perfect square is a natural number which is the square of a natural number.';
// Start MATRICES
var def_matrix_keyword =
'
'
+'Matrix';
var def_matrix_caption =
'Definition
Matrix';
var def_matrix =
' A matrix is a rectangular array of numbers.';
var def_entries =
' The numbers in the array are called entries of the matrix.';
var def_order =
' If a matrix has m rows and n columns, the order of the matrix is m×n.';
var def_square_matrix =
'If the number of rows n is the same as the number of columns, the matrix is a'
+' square matrix and its order is n.';
var def_row_matrix_keyword =
'
'
+'Row Matrix';
var def_row_matrix_caption =
'Definition
Row Matrix';
var def_row_matrix =
'If a matrix has only one row, it is called a row matrix.';
var def_column_matrix_keyword =
'
'
+'Column Matrix';
var def_column_matrix_caption =
'Definition
Column Matrix';
var def_column_matrix =
'If a matrix has only one column, it is called a column matrix.';
var def_main_diagonal_entries =
'For a square matrix, the elements whose row index is the same as the column '
+' index (a11, a22, a33, a44, a55, a66 ... ann)'
+' are called the main diagonal entries.';
var def_augmented_matrix =
'The matrix derived from a system of equations written in standard form with the constant term on the right is called the '
+' augmented matrix.';
var def_coefficient_matrix =
'The matrix consisting of the coefficients (in the same order) of a system of equations is called the '
+' coefficient matrix.';
var def_equality_of_matrices =
'Two matrices are equal if they have the same order and corresponding entries are equal.';
var def_matrix_equality =
'Two matricies A = [aij] and '
+'B = [bij] are equal '
+'if they have the same order and their corresponding entries are equal.';
var def_scalar_keyword =
'
'
+'Scalar';
var def_scalar_caption =
'Definition
Scalar';
var def_scalar =
'A scalar is a real number.';
var def_matrix_opposite_keyword =
'
'
+'Matrix Opposite';
var def_matrix_opposite_caption =
'Definition
Matrix Opposite';
var def_matrix_opposite =
'The opposite of a matrix A = [aij] '
+'is the scalar product (-1)A = [(-1)aij].'
+'
The opposite of a matrix A is usually designated by -A.';
var def_matrix_difference =
'The matrix difference A - B is defined by A - B = A + (-B).
'
+'As always, subtraction is addition of the minuend and the opposite of the subtrahend.';
var def_scalar_product_keyword =
'
'
+'Scalar Product';
var def_scalar_product_caption =
'Definition
Scalar Product';
var def_scalar_product =
'If A = [aij] is a matrix and c is a scalar, the '
+'scalar product cA is the matrix defined by
'
+'cA = [caij]';
var def_matrix_addition_keyword =
'
'
+'Matrix Addition';
var def_matrix_addition_caption =
'Definition
Matrix Addition';
var def_matrix_addition =
' The sum of two matricies '
+' A = [aij] and '
+'B = [bij] of the same order '
+' m×n is the m×n matrix defined by '
+'A + B = [aij + bij].';
var def_matrix_additive_identity =
'The m×n matrix whose entries are all 0 is called a '
+'zero matrix and it is the '
+'additive identity for the set of m×n matrices.'
+' Sometimes O is used as a symbol for the zero matrix.';
var def_matrix_multiplication =
'If A = [aij]m×n is an m×n matrix and '
+'B = [bij]n×p is an n×p matrix, then the '
+'product AB is defined as the m×p matrix '
+'AB = [ai1b1j + ai2b2j + '
+'ai3b3j + … + ainbnj].';
var def_simplified_matrix_multiplication_keyword =
'
'
+'Simplified Matrix Multiplication';
var def_simplified_matrix_multiplication_caption =
'Definition
Simplified Matrix Multiplication';
var def_simplified_matrix_multiplication =
'This product will be computed according to the definition of the product of two matrices.
'
+'The entry in the ithrow and jth column of the product of two matrices '
+' will be the inner product of the ith row from the first matrix and the jth '
+'column of the second matrix.';
var def_inner_product =
'If X = [x1 x2 x3 … xn] '
+'is a row matrix with n entries and
'
+'Y = 
'
+'is a column matrix with n entries, then the inner product (sometimes called dot product) '
+'X•Y is a scalar computed according to the rule: '
+'X•Y = x1y1 + x2y2 + x3y3 + … + xnyn';
var def_matrix_multiplicative_identity =
' The identity matrix of order n is the matrix whose main diagonal entries are 1 '
+'and all other entries are 0. The identity matrix of order n is usually denoted by '
+'In or simply I when the order is obvious.';
var def_determinant =
'The determinant is a function whose domain is the set of '
+'square matricies and whose range is the Real numbers. The range value associated with '
+'a particular matrix is called the determinant of that matrix.';
var def_det_2by2 =
'The rule for the determinant of a 2×2 matrix 
'
+' is given by
det(A) = a11a22 - a12a21.';
var def_det_ahat =
'If A = [aij]n×n is a square matrix of order n×n, and n > 2 '
+'then the matrix Âij is the square matrix of order (n-1)×(n-1) '
+'obtained by deleting the ith row and jth column from the matrix A.';
var def_det_cofactor =
'Let A = [aij]n×n be a square matrix of order n×n with n > 2. '
+'Associated with each entry aij of A is a real number labeled Aij '
+'and called the cofactor of aij.
'
+'The cofactor Aij is computed according to the formula '
+'Aij = (-1)i+jdet(Âij).';
var def_det_nbyn =
'Let A = [aij]n×n with n > 2 be a square matrix. The rule for '
+'the det function is
'
+' det(A)= a11A11 + a12A12 + '
+' … + a1nA1n.
'
+'This is called the cofactor expansion along the first row.';
//Start POLYNOMIALS
var def_term_keyword =
'
'
+'Term';
var def_term_caption =
'Definition
Term';
var def_term =
'A term is a letter, a number, or a product of letters and numbers.';
var def_like_terms_keyword =
'
'
+'Like Terms';
var def_like_terms_caption =
'Definition
Like Terms';
var def_like_terms =
'Two terms are called like terms or similar terms if they have the same variables with the same exponents.';
var def_term_sum_keyword =
'
'
+'Sum of Terms';
var def_term_sum_caption =
'Definition
Sum of Terms';
var def_term_sum =
'The sum of two like terms is the term obtained by '
+'adding their coefficients and keeping the same variables with the same exponents.';
var def_opposite_of_a_term_keyword =
'
'
+'Opposite of a Term';
var def_opposite_of_a_term_caption =
'Definition
Opposite of a Term';
var def_opposite_of_a_term =
'If a term is a number, then its opposite is the number equidistant from '
+'zero but on the other side of zero. If a term contains a variable, then its opposite is formed by '
+'replacing its coefficient with the opposite of the coefficient.';
var def_term_difference =
'The difference of two like terms is the term obtained by '
+'changing the operation to addition and replacing the subtrahend with its opposite and then performing '
+'the addition.';
var def_term_product =
'The product of two terms is the term obtained by '
+'multiplying the coefficients according to normal arithmetic properties and multiplying the variables '
+'according to the laws of exponents.';
var def_term_quotient =
'The quotient of two terms is the expression obtained by '
+'dividing the coefficients according to normal arithmetic properties and dividing the variables '
+'according to the laws of exponents.';
var def_degree_term_keyword =
'
'
+'Degree of a Term';
var def_degree_term_caption =
'Definition
Degree of a Term';
var def_degree_term =
'The degree of a term is the sum of the exponents on the variables.';
var def_coefficient_keyword =
'
'
+'Coefficient';
var def_coefficient_caption =
'Definition
Coefficient';
var def_coefficient =
'The numerical part of a term is called the coefficient of the term (sometimes called the numerical coefficient).';
var def_polynomial_keyword =
'
'
+'Polynomial';
var def_polynomial_caption =
'Definition
Polynomial';
var def_polynomial =
'A polynomial is a term or a sum of terms in which all variables have whole number exponents.';
var def_polynomial_symbolic_keyword =
'
'
+'Polynomial - Symbolic Form';
var def_polynomial_symbolic_caption =
'Definition
Polynomial - Symbolic Form';
var def_polynomial_symbolic =
'A polynomial is an expression which can be written as
'
+'anxn + an-1xn-1 + ... +a1x + a0'
+'
where n is a whole number and each of the coefficients are real numbers.';
var def_leading_term_keyword =
'
'
+'Leading Term';
var def_leading_term_caption =
'Definition
Leading Term';
var def_leading_term =
'The leading term of a polynomial is the term with largest degree.';
var def_leading_coefficient_keyword =
'
'
+'Leading Coefficient';
var def_leading_coefficient_caption =
'Definition
Leading Coefficient';
var def_leading_coefficient =
'The coefficient of the leading term of a polynomial is called the leading '
+'coefficient of the polynomial.';
var def_degree_polynomial_keyword =
'
'
+'Degree of a Polynomial';
var def_degree_polynomial_caption =
'Definition
Degree of a Polynomial';
var def_degree_polynomial =
'The degree of a polynomial is the degree of the leading term.';
var def_constant_term_keyword =
'
'
+'Constant Term of a Polynomial';
var def_constant_term_caption =
'Definition
Constant Term of a Polynomial';
var def_constant_term =
'If a polynomial contains a term which is strictly numerical, it is called the '
+'constant term of the polynomial.';
var def_monomial_keyword =
'
'
+'Monomial';
var def_monomial_caption =
'Definition
Monomial';
var def_monomial =
'A polynomial consisting of a single term is called a monomial.';
var def_monomial_gcf_keyword =
'
'
+'GCF of Two Monomials';
var def_monomial_gcf_caption =
'Definition
GCF of Two Monomials';
var def_monomial_gcf =
'The Greatest Common Factor (GCF) of two or more monomials is the product of all numbers '
+'and letters which divide each of the monomials.';
var def_binomial_keyword =
'
'
+'Binomial';
var def_binomial_caption =
'Definition
Binomial';
var def_binomial =
'A polynomial consisting of two terms is called a binomial.';
var def_trinomial_keyword =
'
'
+'Trinomial';
var def_trinomial_caption =
'Definition
Trinomial';
var def_trinomial =
'A polynomial consisting of three terms is called a trinomial.';
var def_linear_polynomial_keyword =
'
'
+'Linear Polynomial';
var def_linear_polynomial_caption =
'Definition
Linear Polynomial';
var def_linear_polynomial =
'A first degree polynomial is called a linear polynomial.';
var def_quadratic_polynomial_keyword =
'
'
+'Quadratic Polynomial';
var def_quadratic_polynomial_caption =
'Definition
Quadratic Polynomial';
var def_quadratic_polynomial =
'A second degree polynomial is called a quadratic polynomial.';
var def_discriminant =
'The discriminant of a quadratic '
+'ax2 + bx + c is b2 - 4ac. ';
var def_quadratic_equation_two_variables =
'A quadratic equation in two variables is an equation which can '
+'be written in the form y = ax2 + bx + c.';
var def_cubic_polynomial_keyword =
'
'
+'Cubic Polynomial';
var def_cubic_polynomial_caption =
'Definition
Cubic Polynomial';
var def_cubic_polynomial =
'A third degree polynomial is called a cubic polynomial.';
var def_polynomial_sum_keyword =
'
'
+'Polynomial Sum';
var def_polynomial_sum_caption =
'Definition
Polynomial Sum';
var def_polynomial_sum =
'The sum of two polynomials is a polynomial obtained by adding like '
+'terms of the two polynomials.';
var def_polynomial_opposite_keyword =
'
'
+'Opposite of a Polynomial';
var def_polynomial_opposite_caption =
'Definition
Opposite of a Polynomial';
var def_polynomial_opposite =
'The opposite of a polynomial is a polynomial obtained by changing the sign of each '
+'term of the polynomial.';
var def_polynomial_difference_keyword =
'
'
+'Difference of Two Polynomials';
var def_polynomial_difference_caption =
'Definition
Difference of Two Polynomials';
var def_polynomial_difference =
'The difference of two polynomials is a polynomial obtained by changing the '
+'operation to addition, changing the subtrahend to its opposite, and performing the addition.';
var def_polynomial_product_keyword =
'
'
+'Product of Two Polynomials';
var def_polynomial_product_caption =
'Definition
Product of Two Polynomials';
var def_polynomial_product =
'The product of two polynomials is a polynomial obtained by multiplying each term '
+'of the first times each term of the second and adding like terms.';
//Start SETS
var def_set =
'A set is a collection of objects.';
var def_set_element =
'An element of a set is one of the objects in the collection.'
var def_set_universal =
'In a given discussion, the set of all objects under consideration is called the Universal Set.';
var def_set_null =
'The Null Set (or Empty Set) is the set with no elements.
'
+'The standard symbol for the null set is 
';
var def_singleton_set=
'A set which contains exactly one element is called a singleton set.';
var def_roster_method =
'The roster method of specifying a set consists of surrounding the collection of elements with braces.';
var def_set_builder_notation =
'The set builder method of specifying a set has the general form {variable | descriptive statement (or rule) }.
'
+'Notation: The vertical bar ( when used in set builder notation) is always read as "such that".
'
+'Application: Set builder notation is frequently used when the roster method is either inappropriate or inadequate.';
var def_is_in=
'The symbol 
'
+' means "is an element of". '
+'The expression x A means (and is read as) x is an element of A.';
var def_is_not_in=
'The symbol 
'
+' means "is not an element of". '
+'The expression x A means (and is read as) x is not an element of A.';
var def_subset =
'The set A is a subset of the set B if every element of set A is an element of set B.
'
+'Notation: The symbol 
is read as "is a subset of"
'
+'Application: The expression A B is read as "A is a subset of B".';
var def_subset_proper =
'The set A is a proper subset of the set B if every element of set A is an element of set B and B contains some elements which are not elements of A.
'
+'Notation: The symbol 
is read as "is a proper subset of"
'
+'Application: The expression A B is read as "A is a proper subset of B".';
var def_set_union =
'If A and B represent sets then their union is the set of elements which are in A or are in B.
'
+'Notation: The symbol 
is read as "union"
'
+'Application: The expression A B is read as "A union B" or as "the union of A and B".';
var def_set_intersection =
'If A and B represent sets then their intersection is the set of elements which are in A and B.
'
+'Notation: The symbol 
is read as "intersection"
'
+'Application: The expression A B is read as "A intersect B" or as "the intersection of A and B".';
var def_set_keyword =
'
'
+'Set';
var def_set_caption =
'Definition
Set';
var def_set =
'A set is a collection of objects.';
var def_element_of_a_set_keyword =
'
'
+'Element of a Set';
var def_element_of_a_set_caption =
'Definition
Element of a Set';
var def_element_of_a_set =
'An element of a set is one of the objects in the collection.';
var def_symbol_is_an_element_of_keyword =
'
'
+'Symbol: is an element of';
var def_symbol_is_an_element_of_caption =
'Definition
Symbol: is an element of';
var def_symbol_is_an_element_of =
'The symbol 
'
+'means "is an element of"
'
+'The expression x A'
+' is read as
"x is an element of A".';
var def_universal_set_keyword =
'
'
+'Universal Set';
var def_universal_set_caption =
'Definition
Universal Set';
var def_universal_set =
'In a given discussion, the set of all objects under consideration is called the universal set.';
var def_null_set_keyword =
'
'
+'Null Set';
var def_null_set_caption =
'Definition
Null Set';
var def_null_set =
'The null set (or empty set) is the set with no elements.
'
+'The symbol for the empty set is 
';
var def_symbol_subset_keyword =
'
'
+'Symbol: subset';
var def_symbol_subset_caption =
'Definition
Symbol: subset';
var def_symbol_subset =
'The symbol 
'
+'means "is a subset of"
'
+'The expression A B'
+' is read as
"A is a subset of B."';
var def_subset_keyword =
'
'
+'Subset';
var def_subset_caption =
'Definition
Subset';
var xxxdef_subset =
'If each element of a set A is an element of a set B, then A is a subset of B.
'
+'Symbolic Form:
';
var def_symbol_union_keyword =
'
'
+'Symbol: union';
var def_symbol_union_caption =
'Definition
Symbol: union';
var def_symbol_union =
'The symbol '
+'means "union"
'
+'The expression A B'
+' is read as
"A union B."';
var def_union_of_sets_keyword =
'
'
+'Union of Sets';
var def_union_of_sets_caption =
'Definition
Union of Sets';
var def_union_of_sets =
'If A and B represent sets then their union is the set of elements which are in A or are in B.
'
+'Symbolic Form:
';
var def_symbol_intersection_keyword =
'
'
+'Symbol: intersection';
var def_symbol_intersection_caption =
'Definition
Symbol: intersection';
var def_symbol_intersection =
'The symbol '
+'means "intersection"
'
+'The expression A B'
+' is read as
"A intersection B."';
var def_intersection_of_sets_keyword =
'
'
+'Intersection of Sets';
var def_intersection_of_sets_caption =
'Definition
Intersection of Sets';
var def_intersection_of_sets =
'If A and B represent sets then their intersection is the set of elements which are in A and are in B.
'
+'Symbolic Form:
';
var def_cartesian_product_of_sets_keyword =
'
'
+'Cartesian Product of Sets';
var def_cartesian_product_of_sets_caption =
'Definition
Cartesian Product of Sets';
var def_cartesian_product_of_sets =
'If A and B represent sets then the Cartesian Product
A X B is the set of ordered pairs whose first coordinates '
+'are elements of A and whose second coordinates are elements of B.
'
+'Symbolic Form:
';
var def_point_slope_equation =
'The equation for the line through the point (x1, y1)with slope m is'
+' y - y1 = m(x - x1)' ;
var def_slope_intercept_equation =
'The slope_intercept form for the equation of a line is y = mx + b where m and b are real numbers '
+'representing the slope and y-intercept respectively.';
var def_slope_formula =
'The slope of the line through two points '
+'(x1, y1) and (x2, y2)'
+' is given by the formula '
+'
';
var def_multiplicity =
'If f is a function whose rule is given by f(x) = anxn + an-1xn-1 + ... +a1x + a0
'
+'and if (x – a)k is the highest power of (x – a) which is a factor of anxn + an-1xn-1 + ... +a1x + a0
'
+' then a is a zero of multiplicity k of the function f.';
var def_vertical_asymptote =
'The vertical line whose equation is x = a, is a vertical asymptote of the graph of a function f '
+'if any one of the following are true
'
+' f(x) increases without bound as x approaches a from the left
'
+' f(x) increases without bound as x approaches a from the right
'
+' f(x) decreases without bound as x approaches a from the left
'
+' f(x) decreases without bound as x approaches a from the right';
var def_horizontal_asymptote =
'The horizontal line whose equation is y = b, is a horizontal asymptote of the graph of a function f '
+'if any one of the following are true
'
+' f(x) approaches b as x increases without bound
'
+' f(x) approaches b as x decreases without bound
';
var def_oblique_asymptote =
'If f is a rational function whose rule is '
+'
'
+'and the degree of N is 1 more than the degree of D, then f can be expressed in the form '
+'
'
+'where the degree of R is less than the degree of D. In this case the line y = mx + b is an oblique asymptote '
+'for the graph of f.';
//&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& MERBEGALGCHAP1 ########################
var def_algebraic_expression_keyword =
'
'
+'Algebraic Expression';
var def_algebraic_expression_caption =
'Definition
Algebraic Expression';
var def_algebraic_expression =
'An algebraic expression is a number, a variable, or sums, '
+'differences, products, quotients, powers, or roots of variables and numbers.';
var def_variable =
'A variable is a letter or a subscripted letter which '
+'represents a number or any other algebraic expression.';
var def_numerator_keyword =
'
'
+'Numerator';
var def_numerator_caption =
'Definition
Numerator';
var def_numerator =
'The numerator of a fraction is the dividend in the indicated division.';
var def_denominator_keyword =
'
'
+'Denominator';
var def_denominator_caption =
'Definition
Denominator';
var def_denominator =
'The denominator of a fraction is the divisor in the indicated division.';
var def_multiplicative_identity_keyword =
'
'
+'Multiplicative Identity';
var def_multiplicative_identity_caption =
'Definition
Multiplicative Identity';
var def_multiplicative_identity =
'The multiplicative identity is the number 1 because 1 has the property that '
+'1a = a1 = a for every real number a.';
var def_quotient_keyword =
'
'
+'Quotient';
var def_quotient_caption =
'Definition
Quotient';
var def_quotient =
'The quotient of a number a (the dividend) divided by a number b (the divisor) '
+'is a number q (the quotient) such that a = bq';
var def_fraction_keyword =
'
'
+'Fraction';
var def_fraction_caption =
'Definition
Fraction';
var def_fraction =
'A fraction consists of a numerator (top), a denominator (bottom), and the indicated '
+'division of the numerator by the denominator.';
var def_fraction2_keyword =
'
'
+'Fraction';
var def_fraction2_caption =
'Definition
Fraction';
var def_fraction2 =
'A fraction is a number q such that the product of q and the '
+'denominator is equal to the numerator.';
var def_equivalent_fractions_keyword =
'
'
+'Equivalent Fractions';
var def_equivalent_fractions_caption =
'Definition
Equivalent Fractions';
var def_equivalent_fractions =
'Two fractions are equivalent fractions if they represent the same number. '
+'If two fractions 
and '
+'
are equivalent, '
+'we carelessly write 
';
var def_sum_parts_of_keyword =
'
'
+'Parts of a Sum';
var def_sum_parts_of_caption =
'Definition
Parts of a Sum';
var def_sum_parts_of =
' Parts of a Sum 
';
var def_difference_parts_of_keyword =
'
'
+'Parts of a Difference';
var def_difference_parts_of_caption =
'Definition
Parts of a Difference';
var def_difference_parts_of =
' Parts of a Difference 
';
var def_product_parts_of_keyword =
'
'
+'Parts of a Product';
var def_product_parts_of_caption =
'Definition
Parts of a Product';
var def_product_parts_of =
' Parts of a Product 
';
var def_quotient_parts_of_keyword =
'
'
+'Parts of a Quotient';
var def_quotient_parts_of_caption =
'Definition
Parts of a Quotient';
var def_quotient_parts_of =
' Parts of a Quotient 
';
var def_product_of_fractions_keyword =
'
'
+'Product of Fractions';
var def_product_of_fractions_caption =
'Definition
Product of Fractions';
var def_product_of_fractions =
'If '
+'and are fractions, '
+'then their product is defined by 
';
var def_quotient_of_fractions_keyword =
'
'
+'Quotient of Fractions';
var def_quotient_of_fractions_caption =
'Definition
Quotient of Fractions';
var def_quotient_of_fractions =
'If '
+'and are fractions, '
+'then their quotient is defined by '
+'
'
+'
NOTE: ALL Division is done by changing to multiplication.
Always multiply the dividend by the multiplicative '
+'inverse of the divisor.';
var def_sum1_of_fractions_keyword =
'
'
+'Fraction Sum - Same Denominator';
var def_sum1_of_fractions_caption =
'Definition
Fraction Sum - Same Denominator';
var def_sum1_of_fractions =
'If '
+'and 
are fractions, '
+'then their sum is defined by '
+'
';
var def_opposite_of_fraction_keyword =
'
'
+'Opposite of a Fraction';
var def_opposite_of_fraction_caption =
'Definition
Opposite of a Fraction';
var def_opposite_of_fraction =
'The opposite of a number is the number equidistant from zero but on the opposite side of zero.
'
+'There are four ways to represent the opposite of a fraction '
+'
'
+'
';
var def_difference_of_fractions_keyword =
'
'
+'Difference of Fractions';
var def_difference_of_fractions_caption =
'Definition
Difference of Fractions';
var def_difference_of_fractions =
'If '
+'and are fractions, '
+'then the difference '
+'
is defined by '
+'
'
+'
NOTE: ALL Subtraction is done by changing to addition.
Always add the minuend and the '
+'opposite of the subtrahend.';
var def_common_denominator_keyword =
'
'
+'Common Denominator';
var def_common_denominator_caption =
'Definition
Common Denominator';
var def_common_denominator =
'A common denominator of two fractions '
+' '
+'and '
+'is a number which is divisible by both the denominators b and d.';
var def_least_common_denominator_keyword =
'
'
+'Least Common Denominator';
var def_least_common_denominator_caption =
'Definition
Least Common Denominator';
var def_least_common_denominator =
'The least common denominator, called the LCD, of two fractions '
+' '
+'and '
+'is the smallest positive common denominator.';
var def_sum2_of_fractions_keyword =
'
'
+'Fraction Sum - Different Denominator';
var def_sum2_of_fractions_caption =
'Definition
Fraction Sum - Different Denominator';
var def_sum2_of_fractions =
'If '
+'and are fractions, '
+'then their sum is computed by determining a common denominator and replacing '
+'each addend with an equivalent fraction with that common denominator';
var def_fraction_lowest_terms_keyword =
'
'
+'Fraction in Lowest Terms';
var def_fraction_lowest_terms_caption =
'Definition
Fraction in Lowest Terms';
var def_fraction_lowest_terms =
'A fraction has been reduced or is in simplest form or is in lowest terms'
+' if the numerator and denominator have no common factors other than 1.';
var def_complex_fraction_keyword =
'
'
+'Complex Fraction';
var def_complex_fraction_caption =
'Definition
Complex Fraction';
var def_complex_fraction =
'A fraction is a complex fraction if its numerator or its denominator (or both) contains a fraction.';
var def_improper_fraction_keyword =
'
'
+'Improper Fraction';
var def_improper_fraction_caption =
'Definition
Improper Fraction';
var def_improper_fraction =
'A fraction is an improper fraction if its numerator is larger than its denominator.';
var def_mixed_number_keyword =
'
'
+'Mixed Number';
var def_mixed_number_caption =
'Definition
Mixed Number';
var def_mixed_number =
'A mixed number is an integer and a fraction written together as a shorthand for '
+'the sum of the integer and the fraction.';
var def_inequality_terms_keyword =
'
'
+'Fraction';
var def_inequality_lowest_terms_caption =
'Definition
Fraction';
var def_inequality_lowest_terms =
'A fraction is in simplest form or lowest terms'
+' if the numerator and denominator have no common factors other than 1.';
var def_real_number_opposite_keyword =
'
'
+'Opposite of a Real Number';
var def_real_number_opposite_caption =
'Definition
Opposite of a Real Number';
var def_real_number_opposite =
'The opposite of a real number is the number which is equidistant from zero '
+'but on the opposite side of zero. ';
var def_subtraction_meaning_keyword =
'
'
+'Meaning of Subtraction';
var def_subtraction_meaning_caption =
'Definition
Meaning of Subtraction';
var def_subtraction_meaning =
'In all of mathematics, subtraction is defined by a conversion to addition as shown '
+'in this diagram.
';
var def_division_meaning_keyword =
'
'
+'Meaning of Division';
var def_division_meaning_caption =
'Definition
Meaning of Division';
var def_division_meaning =
'In all of mathematics, division is defined by a conversion to multiplication as shown '
+'in this diagram.
';
var def_exponential_expression_keyword =
'
'
+'Exponential Expression';
var def_exponential_expression_caption =
'Definition
Exponential Expression';
var def_exponential_expression =
'An expression of the form an is called an exponential expression.';
var def_exponent_keyword =
'
'
+'Exponent';
var def_exponent_caption =
'Definition
Exponent';
var def_exponent =
'In the exponential expression an, n is the exponent.';
var def_exponent_base_keyword =
'
'
+'Base of an Exponential Expression';
var def_exponent_base_caption =
'Definition
Base of an Exponential Expression';
var def_exponent_base =
'In the exponential expression an, a is the base.';
var def_exponent_natural_number =
'When n is a natural number, the exponential expression an is used to indicate that the '
+'base a is multiplied times itself n times.';
var def_scientific_notation =
'A number is written in scientific notation if it is written as the product of a number '
+'between 1 and 10 and an integer power of 10.';
//&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& MERCOLALGCHAP1 ########################
var def_equation_keyword =
'
'
+'Equation';
var def_equation_caption =
'Definition
Equation';
var def_equation =
'An equation is a mathematical statement which contains an = symbol.';
var def_identity_keyword =
'
'
+'Identity';
var def_identity_caption =
'Definition
Identity';
var def_identity =
'An identity is an equation which is true for every real number in the domain of the variables.';
var def_conditional_equality_keyword =
'
'
+'Conditional Equation';
var def_conditional_equality_caption =
'Definition
Conditional Equation';
var def_conditional_equality =
'A conditional equation is an equation which is true when '
+'some real numbers are substituted for the variables and is false when some real numbers are substituted for the variables.';
var def_conditional_equation =
'A conditional equation is an equation which is true when '
+'some real numbers are substituted for the variables and is false when some real numbers are substituted for the variables.';
var def_contradiction_keyword =
'
'
+'Contradiction';
var def_contradiction_caption =
'Definition
Contradiction';
var def_contradiction =
'A contradiction is an equation that has no real number solution. ';
var def_solution_keyword =
'
'
+'Solution';
var def_solution_caption =
'Definition
Solution';
var def_solution =
'A number (or numbers) that makes an equation true when substituted for the variable (or variables) '
+'is called a solution of the equation.';
var def_solution_set_keyword =
'
'
+'Solution Set';
var def_solution_set_caption =
'Definition
Solution Set';
var def_solution_set =
'The collection of all solutions of an equation is called the solution set of the equation.';
var def_graph_of_equation_keyword =
'
'
+'Graph of an Equation';
var def_graph_of_equation_caption =
'Definition
Graph of an Equation';
var def_graph_of_equation =
'The graph of an equation consists of all the points, and only those points, whose coordinates are solutions of the equation.'
+'
An alternate, but equivalent definition is: The graph of an equation consists of all the points, and only '
+'those points, which satisfy the equation.';
var def_x_intercept_keyword =
'
'
+'x_intercept';
var def_x_intercept_caption =
'Definition
x_intercept';
var def_x_intercept =
'An x-intercept of a graph in the Cartesian Coordinate System'
+' is a point where the graph intersects the x-axis.';
var def_y_intercept_keyword =
'
'
+'y_intercept';
var def_y_intercept_caption =
'Definition
y_intercept';
var def_y_intercept =
'A y-intercept of a graph in the Cartesian Coordinate System '
+'is a point where the graph intersects the y-axis.';
var def_equivalent_equations_keyword =
'
'
+'Equivalent Equations';
var def_equivalent_equations_caption =
'Definition
Equivalent Equations';
var def_equivalent_equations =
'Two equations are equivalent if they have the same solution sets.';
var def_solving_equations_keyword =
'
'
+'Solving Equations';
var def_solving_equations_caption =
'Definition
Solving Equations';
var def_solving_equations =
'The process of finding all the solutions (the solution set) of an equation is called '
+'solving the equation.';
var def_simplest_equation_keyword =
'
'
+'Simplest Equation';
var def_simplest_equation_caption =
'Definition
Simplest Equation';
var def_simplest_equation =
'A simplest equation is an equation which has a single variable on one side of the equal sign and a '
+'single number on the other side.';
var def_linear_equation_one_variable_keyword =
'
'
+'Linear Equation in One Variable';
var def_linear_equation_one_variable_caption =
'Definition
Linear Equation in One Variable';
var def_linear_equation_one_variable =
'A linear equation in one variable is an equation that '
+'can be written in the form ax + b = 0 where a and b are real numbers '
+'with not both a and b equal to zero.';
var def_linear_equation_two_variable_keyword =
'
'
+'Linear Equation in Two Variables';
var def_linear_equation_two_variable_caption =
'Definition
Linear Equation in Two Variables';
var def_linear_equation_two_variable =
'A linear equation in two variables is an equation that can be written in the '
+'form y = mx + b where m and b are real numbers. ';
var def_solution_equation_two_variable=
'A solution of an equation in two variables is an '
+'ordered pair of Real Numbers whose coordinates make the equation true when '
+'substituted for the variables.';
var def_quadratic_equation_one_variable_keyword =
'
'
+'Quadratic Equation in One Variable';
var def_quadratic_equation_one_variable_caption =
'Definition
Quadratic Equation in One Variable';
var def_quadratic_equation_one_variable =
'A quadratic equation in one variable is an equation which may be written in the form
'
+'ax2 + bx + c = 0
'
+'where a, b, and c are real numbers and a is not zero.';
var def_quadratic_equation_two_variable_keyword =
'
'
+'Quadratic Equation in Two Variable';
var def_quadratic_equation_two_variable_caption =
'Definition
Quadratic Equation in Two Variable';
var def_quadratic_equation_two_variable =
'A quadratic equation in two variables is an equation which may be written in the form
'
+' y = ax2 + bx + c
'
+'where a, b, and c are real numbers and a is not zero.';
var def_rational_expression_keyword =
'
'
+'Rational Expression';
var def_rational_expression_caption =
'Definition
Rational Expression';
var def_rational_expression =
'A rational expression is an expression that can be written as the quotient of two polynomials with the '
+'denominator not zero.';
var def_rational_expression_symbolic_keyword =
'
'
+'Rational Expression - Symbolic Form';
var def_rational_expression_symbolic_caption =
'Definition
Rational Expression - Symbolic Form';
var def_rational_expression_symbolic =
'A rational expression is an expression that can be written as
'
+'
'
+' with the denominator not zero.';
var def_domain_of_rational_expression =
'Unless otherwise stated the domain of a rational expression is the largest set of real numbers for which the expression '
+'makes sense.';
var def_complex_rational_expression_keyword =
'
'
+'Complex Rational Expression';
var def_complex_rational_expression_caption =
'Definition
Complex Rational Expression';
var def_complex_rational_expression =
'A complex rational expression is a rational expression whose numerator or denominator (or both) '
+'contains a rational expression. ';
var def_rational_equation_keyword =
'
'
+'Rational Equation';
var def_rational_equation_caption =
'Definition
Rational Equation';
var def_rational_equation =
'A rational equation is an equation which contains one or more rational expressions.';
var def_polynomial_equation_keyword =
'
'
+'Polynomial Equation';
var def_polynomial_equation_caption =
'Definition
Polynomial Equation';
var def_polynomial_equation =
'A polynomial equation is an equation which can be written as
'
+'anxn + an-1xn-1 + ... +a1x + a0 = 0'
+'
where n is a whole number and each of the coefficients are real numbers.';
var def_absolute_value_keyword =
'
'
+'Absolute_Value';
var def_absolute_value_caption =
'Definition
Absolute_Value';
var def_absolute_value =
'The absolute value of a number is its distance from 0 on the number line.
A more precise algebraic definition is:
'
+' 
';
var def_inequality_keyword =
'
'
+'Inequality';
var def_inequality_caption =
'Definition
Inequality';
var def_inequality =
'An inequality is a mathematical statement which contains an inequality symbol.';
var def_solution_inequality_keyword =
'
'
+'Solution of an Inequality';
var def_solution_inequality_caption =
'Definition
Solution of an Inequality';
var def_solution_inequality =
'A number (or numbers) that makes an inequality true when substituted for the variable (or variables) is '
+'called a solution of the inequality.';
var def_solution_set_inequality_keyword =
'
'
+'Solution Set of an Inequality';
var def_solution_set_inequality_caption =
'Definition
Solution Set of an Inequality';
var def_solution_set_inequality =
'The collection of all solutions of an inequality is called the '
+'solution set of the inequality.';
var def_equivalent_inequality_keyword =
'
'
+'Equivalent Inequalities';
var def_equivalent_inequality_caption =
'Definition
Equivalent Inequalities';
var def_equivalent_inequality =
'Two inequalities are equivalent inequalities if they '
+'have the same solution sets.';
var def_solving_inequality_keyword =
'
'
+'Solving Inequalities';
var def_solving_inequality_caption =
'Definition
Solving Inequalities';
var def_solving_inequality =
'The process of finding all the solutions (the solution set) of an inequality is called '
+'solving the inequality.';
var def_simplest_inequality_keyword =
'
'
+'Simplest Inequalities';
var def_simplest_inequality_caption =
'Definition
Simplest Inequalities';
var def_simplest_inequality =
'A simplest inequality is an inequality which has a single variable on one side of the inequality symbol and '
+'a single number on the other side.';
var def_graph_inequality_keyword =
'
'
+'Graph of an Inequality';
var def_graph_inequality_caption =
'Definition
Graph of an Inequality';
var def_graph_inequality =
'The graph of an inequality consists of all the points, and only those points, whose '
+'coordinates are solutions of the inequality.'
+'
An alternate, but equivalent definition is:
The graph of an inequality consists of all the points, '
+'and only those points, whose coordinates satisfy the inequality.';
var def_compound_inequality =
'A compound inequality is two inequalities joined by either '
+'the conjunction and or the conjunction or.';
var def_compact_compound_inequality =
'A compact compound inequality is a compound inequality '
+'which can be written in the form a < x < b.';
var def_linear_inequality_one_variable_keyword =
'
'
+'Linear Inequality in One Variable';
var def_linear_inequality_one_variable_caption =
'Definition
Linear Inequality in One Variable';
var def_linear_inequality_one_variable =
'A linear inequality in one variable x is an inequality which can be written in the form '
+'ax + b < 0.';
var def_linear_inequality_two_variable =
'A linear inequality in two variables'
+' x and y is an inequality which can be written as
'
+'y < mx + b or '
+'y > mx + b.';
var def_solution_inequality_two_variable_keyword =
'
'
+'Solution of an Inequality in Two Variables';
var def_solution_inequality_two_variable_caption =
'Definition
Solution of an Inequality in Two Variables';
var def_solution_inequality_two_variable=
'A solution of an inequality in two variables is an '
+'ordered pair of Real Numbers whose coordinates make the inequality true when '
+'substituted for the variables.';
var def_solution_set_inequality_two_variable_keyword =
'
'
+'Solution Set of an Inequality in Two Variables';
var def_solution_set_inequality_two_variable_caption =
'Definition
Solution Set of an Inequality in Two Variables';
var def_solution_set_inequality_two_variable =
'The collection of all solutions of an inequality is called the solution set '
+'of the inequality.';
var def_graph_inequality_two_variable_keyword =
'
'
+'Graph of an Inequality in Two Variables';
var def_graph_inequality_two_variable_caption =
'Definition
Graph of an Inequality in Two Variables';
var def_graph_inequality_two_variable =
'The graph of an inequality consists of all the points, and only those points, whose coordinates are solutions of the inequality.'
+'
An alternate, but equivalent definition is: The graph of an equation consists of all the points, and only '
+'those points, which satisfy the inequality.';
var def_boundary_line_inequality_two_variable_keyword =
'
'
+'Boundary Line of an Inequality in Two Variables';
var def_boundary_line_inequality_two_variable_caption =
'Definition
Boundary Line of an Inequality in Two Variables';
var def_boundary_line_inequality_two_variable =
'If the inequality symbol in an inequality in two variables is replaced with an equality symbol, the graph of '
+'the resulting equation is called the boundary curve for the inequality.';
var def_solution_equation_in_two_variable=
'An ordered pair (x, y) of real numbers is a solution of an '
+'equation in two variables if the coordinates satisfy the equation. '
+'(that is, if a true statement results when the coordinates are substituted for the '
+'variables in the equation.)';
var def_solution_inequality_in_two_variable=
'An ordered pair (x, y) of real numbers is a solution of an '
+'inequality in two variables if the coordinates satisfy the inequality. '
+'(that is, if a true statement results when the coordinates are substituted for the '
+'variables in the inequality.)';
var def_quadratic_inequality_one_variable_keyword =
'
'
+'Quadratic Inequality in One Variable';
var def_quadratic_inequality_one_variable_caption =
'Definition
Quadratic Inequality in One Variable';
var def_quadratic_inequality_one_variable =
' A quadratic inequality in one variable is an inequality which may be written in the form
'
+'ax2 + bx + c < 0
'
+'where a, b, and c are real numbers and a is not zero.';
var def_polynomial_inequality_keyword =
'
'
+'Polynomial Inequality';
var def_polynomial_inequality_caption =
'Definition
Polynomial Inequality';
var def_polynomial_inequality =
'A polynomial inequality is an inequality which may be written in the form
'
+' 
';
var def_rational_inequality_keyword =
'
'
+'Rational Inequality';
var def_rational_inequality_caption =
'Definition
Rational Inequality';
var def_rational_inequality =
'A rational inequality is an inequality which may be written in the form
'
+' 
';
var def_square_root_of_a_nonnegative_number =
'If k is a positive real number then the principal square root '
+' of k is a positive number whose square is k.
The opposite of the principal '
+'square root is also a square root of k. It is called the negative square root of k. ';
var def_principal_square_root_of_a_negative_number_keyword =
'
'
+'Principal Square Root of a Negative Number';
var def_principal_square_root_of_a_negative_number_caption =
'Definition
Principal Square Root of a Negative Number';
var def_principal_square_root_of_a_negative_number =
'If k is a positive real number then the principal square root of its opposite -k is defined by'
+' 
';
var def_divisible_natural_number =
'If the remainder r in the division algorithm is 0, then we say that a is '
+'divisible by b.';
var def_divisible_polynomial =
'If the remainder r in the division algorithm is 0, then we say that the polynomial p is '
+'divisible by the polynomial d.';
// Start SYSTEMS OF EQUATIONS AND INEQUALITIES
var def_system_of_equations =
'A system of equations consists of '
+'two or more equations involving the same variables.';
var def_solution_for_system_of_equations =
'A solution for a system of '
+'equations is an ordered n-tuple of numbers which satisfy all of the equations '
+'in the system of equations.';
var def_solution_set_for_system_of_equations =
'The collection of all solutions of a system of equations '
+'is called the solution set of the system of equations.';
var def_solving_system_of_equations =
'The process of finding all the solutions (the solution set) of a system of equations is called '
+'solving the system of equations.';
var def_equivalent_systems_of_equations =
'Two systems of equations are '
+'equivalent systems if they have the same solution sets.';
var def_to_factor =
'To factor a number or algebraic expression '
+'means to write the number or expression as a product.';
var def_factorization =
'When a number or algebraic expression is factored, written as a product, the indicated '
+'product is called a factorization of the number or algebraic expression ';
var def_right_triangle =
'A triangle with one right angle is a right triangle. ';
var def_hypotenuse =
'The hypotenuse of a right triangle is the side opposite the right angle. ';
var def_legs_triangle =
'Sides adjacent to the right angle in a right triangle are called legs of the triangle.';