Introduction to Sets and Set Notation

This set of flashcards covers the fundamental definitions and notations of set theory as presented in the lecture notes, including roster notation, cardinality, and various set types.

Set

A collection of objects made up of specified elements, or members.

Roster notation

A way to describe a set by listing all of the elements in the set, surrounded by braces and seperated by commas, such as $A = \{1, 2, 3, 4\}$.

Equal sets

Sets that contain exactly the same elements; if sets $A$ and $B$ are equal, it is written as $A = B$.

Cardinal number (cardinality)

The number of elements contained in a finite set, denoted by $| |$.

Equivalent sets

Sets that have the same cardinal number, or the same number of elements, denoted by the notation $C \sim D$.

Set-builder notation

A notation used to describe a set when the members all share certain properties, for example $J = \{x | x \in N, x < 10\}$.

Empty set (null set)

A set that contains no elements, denoted by $\Phi$.

Universal set

The set of all elements being considered for any particular situation, denoted by $U$.

Complement of A

Consits of all the elements in the given universal set that are not contained in $A$, denoted by $A'$.