Number Systems and Set Theory

Flashcards covering basic terms, definitions, and concepts related to number systems and set theory for MATH 1115.

Set

A well-defined collection of distinct objects, called elements.

Natural Numbers (N)

The set of natural numbers, typically including 0 and positive integers: N = {0, 1, 2, 3, …}.

Set-builder Notation

A notation for describing a set by specifying a property that its members must satisfy, often written as { x | x has property P }.

Membership

The relation indicating that an element x is part of a set A, denoted x ∈ A.

Subset

A set B is a subset of A (written B ⊆ A) if every element of B is also in A.

Proper Subset

A set B is a proper subset of A (written B ⊂ A) if B is a subset of A but not equal to A.

Union (A ∪ B)

The set containing all elements that are in A or B.

Intersection (A ∩ B)

The set containing all elements that are common to both A and B.

Relative Complement (A \ B)

The set containing elements in A that are not in B.

Real Numbers (R)

The set of all numbers that can represent a distance along a continuous line, including both rational and irrational numbers.

Complex Numbers (C)

Numbers that include a real part and an imaginary part, represented as C = { p + qi | p, q ∈ R }.

Rational Numbers (Q)

Numbers that can be expressed as a ratio of two integers, where the denominator is not zero.

Irrational Numbers

Numbers that cannot be expressed as a ratio of integers; they have non-terminating, non-repeating decimal expansions.

Density of Rational and Irrational Numbers

A property where between any two real numbers, there exists both a rational and an irrational number.

Venn Diagram

A visual representation of the relationships between different sets, often using overlapping circles.