Xref: utzoo comp.ai:2680 talk.philosophy.misc:1602
Path: utzoo!attcan!uunet!husc6!bloom-beacon!mit-eddie!uw-beaver!teknowledge-vaxc!sri-unix!garth!smryan
From: smryan@garth.UUCP (Steven Ryan)
Newsgroups: comp.ai,talk.philosophy.misc
Subject: Re: Artificial Intelligence and Intelligence
Message-ID: <1923@garth.UUCP>
Date: 22 Nov 88 00:48:41 GMT
References: <1919@garth.UUCP> <2671@uhccux.uhcc.hawaii.edu>
Reply-To: smryan@garth.UUCP (Steven Ryan)
Organization: INTERGRAPH (APD) -- Palo Alto, CA
Lines: 34

>" Just a short note that is a mortal sin for a mathematician to say
>" `arb***ry.' Penance usually is usually five Hail Davids.
>" 
>" The word `infinite' only occurs before `set,' `infinite set,' where it has
>" a very precise meaning.
>" 
>" The correct term is `arbitrary.'
>
>Now it makes even more sense.

Without wanting to start a jihad, but in most math and computer science, there
is a real attempt to avoid the word `infinity' and `infinite' really is
restricted to `infinite set.'

That little thing that looks like a propellor is read as `unbounded':
x -> oo, f(x) -> oo. `As x increases unbounded, f at x increases unbounded.'

The problem is that `infinity' is such a transcendental kind of word, that any
attempt to define it causes problem. Aleph-0 is an infinite set, but
2**aleph-0=aleph-1 is an even larger infinite set. If we try to define
infinity as the largest possible set, then we are left with
infinity=2**infinity.

`Arbitrary' means the same, more or less, as `unbounded.'

Finally, note that `unbounded' does not always mean infinite. If a Turing
machine accepts, its tape is unbounded, but it must be finite.
-- 
                                                   -- s m ryan
+---------------------------------------------------------------+--------------+
| And they looked across the PDP7 and saw that it was idle and  |  OSF is the  |
| without users. They `said let there be code' and it was.      |  antiUnix.   |
+---------------------------------------------------------------+--------------+
  There was a read and a write and it was the first memory cycle.