Date: Thu, 25 Sep 1997 21:44:49 +1000 From: Bruce Evans <bde@zeta.org.au> To: bde@zeta.org.au, tlambert@primenet.com Cc: current@FreeBSD.ORG, gibbs@plutotech.com, julian@whistle.com, nate@mt.sri.com Subject: Re: new timeout routines Message-ID: <199709251144.VAA13138@godzilla.zeta.org.au>
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I wrote:
>> This was an invalid assumption, since timeout() was only (almost)
>> nilpotent (calling it N+1 times has the same effect as calling it N
>> times for some value of N, provided there are no calls to timeout()
>> mixed with the calls to untimeout()).
Oops. Nilpotence (for an element x in a ring) is actually x^N == 0,
not x^(N+1) == x^N.
>> Now it is (almost) idempotent (N = 1 in the above), provided the
This is correct. Idempotence (for an element x in a set with a binary
operation '*') is x*x = x.
>Actually, this is "called reflexively".
Wrong. Reflexivity (for an element x in a set with a binary relation
R to itself) is xRx.
> Main Entry: idempotent
> Pronunciation: 'I-d&m-"pO-t&nt
> Function: adjective
> Etymology: Latin idem same + potent-, potens having power -- more at
> POTENT
> Date: 1870
> : relating to or being a mathematical quantity which when applied to
> itself under a given binary operation (as multiplication) equals
> itself; also : relating to or being an operation under which a
> mathematical quantity is idempotent
> - idempotent noun
This is correct :-). There must be a binary operation (i.e., a mapping
SxS -> S), not just a self-relation (i.e., a mapping SxS -> {0, 1}) to
define idempotence.
Bruce
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