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August 25th, 2010

special finite cardinals

Zero is special because it's the number of things you have if you don't have anything.

One is special because it's not zero.

Two is special because an alphabet of two symbols allows exponentially shorter representations of objects than an alphabet of only one symbol.

Three is special because an alphabet of three symbols allows infinite non-repeating (EDIT: square-free, to be precise) strings, but an alphabet of two symbols does not.

Is four special?*

* other than for being the smallest number not otherwise special, smartass