Set Theory - Algebra II

N

N

Natural (1, 2, 3, ...)

W

Whole (0, 1, 2, ...)

Z

Integers (-1, 0, 1, ...)

Q

Rational

I

Irrational

R

Real

Closure

If you perform an operation on two numbers within one set of numbers the solution is also in the same set of numbers

Commutativity

a+b=b+a, xy=yx

Associativity

The parentheses in an all addition or all multiplication equation does not have an effect on the solution

Identity Element

0 for addition, 1 for multiplication

Inverse Element

Addition-Subtraction, Multiplication-Division

List Method

{x, y, z, ...}

Set-builder Notation

{x | x > 0}

Equality

Same elements

Equivalence

Same number of elements

cardinality

The number of elements in a set

Number of Possible Subsets in a Set

2^n, where n = number of elements