| A | B |
|---|
| {a,b} | the set containing elements a and b |
| {} | the empty set |
| {x|x has property P} | the set of all numbers x, such that x has property P |
| |x| | the absolute value of x |
| a < b | the number a is less than the number b |
| a > b | the number a is greater than the number b |
| (a,b) | the interval {x|a<x<b} |
| set | a defined collection of objects or elements |
| natural numbers | {1,2,3,4,5,6,7,...} |
| whole numbers | {0,1,2,3,4,5,6,7,...} |
| integers | {...-2,-1,0,1,2,...} |
| rational numbers | {x|x has a terminating or repeating decimal representation} |
| irrational numbers | {x|x has a nonterminating, nonrepeating decimal representation} |
| real numbers | {x|x is represented by a point on a number line} |
| -a | the additive inverse of the number a |
| -(-a)= ? | a |
| |a| = | a if a is positive or 0; -a if a is negative |
| a < b if | a is to left of b on a number line |
| a > b if | a is to right of b on a number line |
| distance between two numbers | absolute value of the difference between the numbers |
| a - b = | a + (-b) for all real numbers |
| the sum of two positive real numbers is | a positive number |
| the sum of two negative real numbers is | a negative number |
| the sum of a positive and a negative real number | has the sign of the number with the largest absolute value |
| the product of two real numbers with the same sign is | a positive number |
| the product of two real numbers with opposite signs is | a negative number |
| a/b = q if and only if | a = bq |
| division by zero is | undefined |
| a/b = | a * (1/b) for all real numbers, b not zero |
| distributive property of multiplication over addition | a(b+c) = ab + ac |
| distributive property of addition over multiplication | (b+c)a = ba + ca |
| additive identity | 0 |
| multiplicative identity | 1 |
| additive inverse of a | -a |
| multiplicative inverse of a | 1/a |
| commutative property of addition | a + b = b + a |
| commutative property of multiplication | ab = ba |
| associative property of addition | a + (b + c) = (a + b) + c |
| associative property of multiplication | a(bc)=(ab)c |
| multiplication property of 0 | for all real numbers a, a*0 = 0 |
