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von Neumann ordinals

In the area of mathematics called set theory, a specific construction due to John von Neumann[39][40] defines the natural numbers as follows:

  • 0 = { },
  • 1 = 0 ∪ {0} = {0} = {{ }},
  • 2 = 1 ∪ {1} = {0, 1} = {{ }, {{ }}},
  • 3 = 2 ∪ {2} = {0, 1, 2} = {{ }, {{ }}, {{ }, {{ }}}},
  • n = n−1 ∪ {n−1} = {0, 1, ..., n−1} = {{ }, {{ }}, ..., {{ }, {{ }}, ...}}, etc.

With this definition, a natural number n is a p

von Neumann ordinals

In the area of mathematics called set theory, a specific construction due to John von Neumann[39][40] defines the nat

In the area of mathematics called set theory, a specific construction due to John von Neumann[39][40] defines the natural numbers as follows: