Mathematics Study Manual: Sets and the Number System

A collection of flashcards covering fundamental concepts in set theory and the number system, including definitions and important terms.

Set

A well-defined collection of distinct objects.

Element

An object belonging to a set, indicated by x ∈ A.

Subset

A set whose every element is contained in another set, indicated by A ⊆ B.

Empty set

A set containing no elements, written as ∅.

Union

The set formed by combining all elements from two sets, written A ∪ B.

Intersection

The set containing only elements common to both sets, written A ∩ B.

Difference

The set of elements in one set that are not in another, written A - B.

Complement

Elements in the universal set U that are not in set A, written A'.

Natural Numbers (N)

Counting numbers starting from 1: 1, 2, 3, … (some definitions include 0).

Whole Numbers (W)

Natural numbers along with 0.

Integers (Z)

All whole numbers including negative numbers: …, -3, -2, -1, 0, 1, 2, 3, …

Rational Numbers (Q)

Numbers that can be expressed as the fraction p/q where p and q are integers and q ≠ 0.

Irrational Numbers

Real numbers that cannot be expressed as p/q; their decimal representation is non-terminating and non-repeating.

Real Numbers (R)

All rational and irrational numbers that can be found on the number line.

Cardinality

The number of elements in a set, denoted n(A).

Roster Notation

Describing a set by listing its elements, for example, A = {1, 2, 3, 4}.

Set-builder Notation

Describing a set by stating a property that its elements satisfy, for example, B = {x | x is an even natural number less than 10}.