Ordinal Addition/Examples
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Examples of Ordinal Addition
Ordinal Addition by One
Let $x$ be an ordinal.
Let $x^+$ denote the successor of $x$.
Let $1$ denote (ordinal) one, the successor of the zero ordinal $\O$.
Then:
- $x + 1 = x^+$
where $+$ denotes ordinal addition.
Ordinal Addition by Two
Let $2$ denote the successor of the ordinal $1$.
Then:
- $x + 2 = x^{++}$
Ordinal Addition by Natural Number
Let $n$ be a natural number.
Then:
- $x + \paren {n + 1} = \paren {x + n}^+$