48 lines
1.4 KiB
Plaintext
48 lines
1.4 KiB
Plaintext
From: gmcm at hypernet.com (Gordon McMillan)
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Date: Tue, 18 May 1999 23:55:04 -0500
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Subject: while (a=b()) ... infinite sets digression
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In-Reply-To: <3742228D.7B5C@cosc.canterbury.ac.nz>
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Message-ID: <1285032566-173470670@hypernet.com>
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Content-Length: 1154
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X-UID: 1904
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Greg Ewing wrote:
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> Chad Netzer wrote:
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> >
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> > So, there are infinitely more strings which start with underscores than do not,
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>
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> Hmmm... this would seem to imply that there are
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> infinitely many more strings starting with any
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> given character than any other character.
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>
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> Which seems absurd. Although where infinities
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> are involved, that doesn't necessarily mean it's
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> not true...
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>
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> Tricky and dangerous beasts, these infinities!
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Unfortunately, Chad mispoke. For any string beginning with an
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underscrore there are (num_possible_characters-1) strings not
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beginning with an underscore (just replace that first character).
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But if there are Aleph-nought strings beginning with underscore,
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there are N*Aleph-nought == Aleph-nought not beginning with
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underscore.
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Chad's trickery is in trying to get you to assume that Aleph-nough
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minus Aleph-nought is 0. Nice try.
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All this assumes, of course, that you allow strings of infinte
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length. Personally, I don't. And since strings don't have sides, you
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can't even fake one by folding a finite-lengthed one into a Mobius
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string.
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though-some-forms-of-Unicode-come-close-ly y'rs
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- Gordon
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