Sets 8th Grade Math Algebra I Honors

Rational Numbers

Q Any number that can be expressed as a fraction

Real Numbers

R all irrational and rational #s

RIQZWN

REAL IRRATIONAL Q RATIONAL Z INTEGERS WHOLE NATURAL

complements

can be represented as: A^c A' ~A Ā complement + original = what the complement is of, for example B= {1,2,3} A={1} Ā={2,3} A+Ā=B

inclusive

contains ALL endpoints, CLOSED circles

exclusive

contains NO endpoints, OPEN circles

Venn Diagram in Math

if circles are inside each other: the inner circle must also meet the rules of the outer circle Always put name/number on top outside of circles doesn't have the characteristics needed remember to count the overlapping stuff Challenge: A={1,2,3,4,5} B={2,4,5} C={1,2,14} (A ∩ B) U C = {1,2,4,14}

roster form

lists the elements of a set within braces

And

overlap/showing what is in common in between inequalities. {x: 2<x<5}

Multiples of 6 between 6 and 36 inclusive set H

H={6x: x E N 1 ≤ x ≤ 6}

Irrational Numers

I Non-terminating decimals with no repitition. ex: square root of 2.

Natural Numbers

N The set of numbers without 0: 1, 2, 3, 4, ... Also called counting numbers.

half-closed

ONE, but not another endpoint contained one circle open, one circle closed

disjunction

OR

conjunction

AND

Intersection

"and" ∩ excludes things that aren't in common Ex: A ∩ B=6 A={5,6,8} B={6,9,10} Ex: A ∩ B={x: x < 3} A= x<5 B= x<3 Ex: A ∩ B=[5,6] A= [5, infinity) B= (3, 6]

Union

"or" U all things in both sets together Ex: A U B={5,6,8,9,10} A={5,6,8} B={6,9,10} Ex: A U B={x: x < 5} A= x<5 B= x<3 Ex: A ∩ B=(3, infinity) A= [5, infinity) B= (3, 6]

interval notation

A notation for describing an interval on a number line. The interval's endpoint(s) are given, and a parenthesis or bracket is used to indicate whether each endpoint is included in the interval. brackets mean that they are included parenthesis mean that they are not included -infinity is always in parenthesis- (-3, 2] is equal to {x: -3<x≤2} *in interval notation, or is a U*

set-builder notation

A notation used to describe the elements of a set {x | x>2} or {x: x>2} or is a V { x: x>2 V x< -1}

Equivalent

Same # of elements

Equal

The same

Whole Numbers

W Natural numbers ( counting numbers) and zero; 0, 1, 2, 3...

Integers

Z The set of whole numbers and their opposites ...-2, -1, 0, 1, 2...

null (empty) set

a set that contains no elements the null set is a subset of all sets { } or empty set or null ser or symbol in picture

subset

a set that is part of a larger set any set is a subset of itself the empty set is a subset of all sets A= {1,2,3} B={2} A is a subset of B

elements

∈ means "is an element of" elements are members of a set A= {x: x ∈ set of natural numbers and x<0} the answer to that would be the empty set because there are no natural numbers less than 0