From Cantor's Attic
Revision as of 18:18, 10 January 2017 by Trixie Wolf (Added some detail to definition, and removed a couple of mistaken statements (the collection of all ordinals is not a set, for one).)
Given an ordinal (or cardinal) $x$:
- $x + 0 = 0 + x = x$.
- $x \cdot 0 = 0 \cdot x = 0$
- $x^0 = 1$
- $0^x = 0$ (if $x > 0$)
Some set theorists (e.g. Thomas Jech) instead classify zero as a limit ordinal, because like other limit ordinals, it is the limit of all ordinals less than it (of which there are none).