On Apr 16, 4:58 pm, Rich Hutnik wrote:
On Apr 15, 3:53 pm, Quadibloc wrote:



On Apr 12, 11:08 pm, Rich Hutnik wrote:

But, if one is working with Chess Variants, then the issue does
arise that if the number of variants is finite, then you can have a
classification system in place that could capture them all, and even
simplify, and perhaps bridge them.

I think that one can always go 'outside the system' and come up with a
reasonable new Chess variant that is not included in any
classification system, even if that system embraces an infinite number
of variants.

Yet, the fact that people can only handle games up to a certain finite
level of complexity means that the number of Chess variants is finite.

A large, but poorly-defined finite set, therefore, can behave for
practical purposes as if it had properties that, in an exact
mathematical sense, can only apply to a set with at least aleph-one
elements. This doesn't defy any law of mathematics (and, indeed, due
to the subject matter, I've pulled sci.math back in, since it's
relevant now).

John Savard

So, then, to make this more mathematical, are the number of rules
variants for a game like chess an Aleph of any sort? I will this
topic to have it ask that. Maybe someone else who is more math(y) in
their knowledge could frame this in a more mathematically proper form.

- Rich

It is relatively simple to come up with an infinite number of
variants.
Consider that in standard chess the king can be captured by a single
attack. Consider a variant where the king can only be captured by
two attacks. This generalizes to 3,4,...,n,... attacks.

(Actually, Simon Smith's argument above falls a bit short. It is
not enough to show there are an infinite number of descriptions
of variants of Calvinball chess (after all for each variant there
are an infinite number of descriptions))

- William Hughes