Set notation

A set can be described intensionally or extensionally.

An intensional definition gives the meaning of a term by specifying necessary and sufficient conditions for when the term should be used.

An extensional definition gives the meaning of a term by specifying its extension, i.e. specifying every object that falls under the definition of the term in question.

Set notations:

• sets are implicitly denoted using capital letters

• sets are explicitly denoted using braces

• Intensional set definition

  • semantic declaration: "a set containing odd natural numbers"

  • roster notation: directly enumerating its elements, {2,4,6,8,10}

    • finite sets may use ellipsis and a terminal element

    • infinite set may use ellipsis

• Extensional set definition

  • set-builder notation: lists properties and conditions members must satisfy