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Results tagged with ordinal-numbers
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user 40324
An ordinal is the order type of a well-ordered set. The first few ordinals are $0, 1, 2, \dots, \omega, \omega+1, \dots$ where $\omega$ is the order type of $\mathbb{N}$, and $\omega+1$ is the order type of $\mathbb{N}$ together with a maximum element.
1
vote
Finite Number of Registers and Computable Well-Orderings
For question 2(A), one register can of course only be the predecessor function so you can only go up to $\omega$. For $n$ registers with $n \ge 2$, the ordinal $\varphi(n-1,0)$ is the highest ordinal …
- 141
3
votes
Anything known about the Grundy Ordinal of Sylver's Coinage
One thing we do know about the Grundy number of a position is that it is less than or equal to the ordinal representing the maximum length of the game starting from that position; to be precise, defin …
- 141