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Date: Thu, 25 Sep 1997 21:44:49 +1000
From: Bruce Evans <bde@zeta.org.au>
Message-Id: <199709251144.VAA13138@godzilla.zeta.org.au>
To: bde@zeta.org.au, tlambert@primenet.com
Subject: Re: new timeout routines
Cc: current@FreeBSD.ORG, gibbs@plutotech.com, julian@whistle.com,
        nate@mt.sri.com
Sender: owner-freebsd-current@FreeBSD.ORG
X-Loop: FreeBSD.org
Precedence: bulk

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