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Ordinal Number

Ordinal Number

Dec 10, 20251 min read

  • math/set

Definition

ord(A)=o(A)

Operations

Addition

A∩B=∅⇒o(A)+o(B)=o(A∪B)

Associative Property: (α+β)+γ=α+(β+γ)

Multiplication

o(A)o(B)=o(B×A)

Associative Property: α(βγ)=(αβ)γ

left Distributive Property: α(β+γ)=αβ+αγ

Facts

∀A:∃!o(A) where A is a Well-Ordered Set

∀a:∃A,o(A)=a where A is a Well-Ordered Set and a is an ordinal number

∣A∣=∣B∣⇔o(A)=o(B)

A=∅⇔o(A)=0

o(N)=ω


Graph View

  • Definition
  • Operations
  • Addition
  • Multiplication
  • Facts

Backlinks

  • Set Theory Note

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