[FOM] Re: counting arguments
Timothy Y. Chow
tchow at alum.mit.edu
Wed Oct 29 20:11:42 EST 2003
Alasdair Urquhart wrote:
> I think it is rather trivially true that any probabilistic argument in
> finite combinatorics can be rewritten as a counting argument. This is
> because probability in finite spaces is simply the ratio of two finite
> cardinalities.
Maybe this is just a semantic quibble, but to me, the adjective "finite"
in the phrase "probabilistic argument in finite combinatorics" indicates
only that the subject matter and the statement of the theorems are finite,
not that the probabilistic argument itself is necessarily finitary. So,
I would classify finitary combinatorial theorems whose proofs are
probabilistic and that take infinitary detours as "probabilistic arguments
in finite combinatorics." These might not reduce to counting, in any
reasonable sense of the word.
Tim
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