| A | B |
|---|
| Absolute value | A number's distance from zero on the number line |
| Addition Property of Equality | if a = b, then a + c = b + c |
| Addition Property of Inequality | if a > b, then a + c > b + c; if a < b, then a + c < b + c |
| Algebraic expression | Expression that contains at least one variable |
| Associative Property of Addition | (a + b) + c = a + (b + c) |
| Associative Property of Multiplication | (ab)(z) = (a)(bz) |
| Commutative Property of Addition | a + b = b + a |
| Commutative Property of Multiplication | ab = ba |
| compound inequality | two inequalities joined by the word AND or OR |
| counterexample | Specific case that shows that a statement is false |
| Distributive Property | a(b + c) = ab + ac and (b + c)a = ba + ca |
| Division Property of Equality | if a = b, then a / c = b / c |
| Division Property of inequality (c pos) | if a > b, a/c > b/c if a < b, then a/c < b/c |
| Division Property of inequality (c neg) | if a > b, a/c < b/c if a < b, then a/c > b/c |
| empty set | Solution set for an equation that has no solution |
| equation | Mathematical sentence stating that two mathematical expressions are equal |
| formula | Mathematical sentence that expresses the relationship between certain quantities |
| Identity Property of Addition | a + 0 = a = 0 + a |
| Identity Property of Multiplication | (a)(1) = a = (1)(a) |
| intersection | Graph of a compound inequality containing AND |
| interval notation | Using positive or negative infinity symbols to indicate that the solution set of an inequality is unbounded in the positive or negative directions, respectively |
| Inverse Property of Addition | a + (-a) = 0 = (-a) + (a) |
| Inverse Property of Multiplication | If a is not zero, (a)(1/a) = 1 = (1/a)(a) |
| irrational numbers | Real number that is not rational. The decimal form neither terminates nor repeats. |
| Multiplication Property of Equality | if a = b, then ac = bc |
| Multiplication Property of Inequality (c pos) | if a > b, then ac > bc if a < b, then a/c < b/c |
| Multiplication Property of Inequality (c neg) | if a > b, then ac < bc if a < b, then ac > bc |
| open sentence | Mathematical sentence containing one or more variables |
| order of operations | P E M D A S |
| rational numbers | Number m/n, where m and n are integers and n is not zero; decimal form either repeats or terminates |
| real numbers | All numbers used in everyday life; the set of all rational and irrational numbers |
| Reflexive Property | a = a |
| set-builder notation | Expression of the solution set of an inequality, for example {X l x > 9} |
| solution | Replacement for the variable in an open sentence that results in a true sentence |
| Substitution Property | if a = b, then a may be replaced by b and b may be replaced by a |
| Subtraction Property of Equality | if a = b, then a - c = b - c |
| Subtraction Property of Inequality | if a > b, then a - c > b - c; if a < b, then a - c < b - c |
| Symmetric Property | if a = b then b = a |
| Transitive Property | if a = b and b = c, the a = c |
| Trichotomy Property | property of order: a < b or a = b or a > b |
| union | Graph of a compound inequality containing OR |
| variable | Symbols, usually letters, used to represent unknown quantities |
