Re: Humble pie.
From: Arturo Magidin (magidin_at_math.berkeley.edu)
Date: 06/25/04
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Date: Fri, 25 Jun 2004 21:25:58 +0000 (UTC)
In article <XV%Cc.64$kf2.34@newsfe3-gui>,
Andrew <stan370@btinternet.com> wrote:
>
>"Arturo Magidin" <magidin@math.berkeley.edu> wrote
>
>>
>> Yes: each natural number is finite; however, the set of all natural
>> numbers is infinite.
>>
>
>I would like to proceed very carefully here.
>
>Since you agree that each natural number is finite thought the set of
>natural numbers is infinite, would I be fair in thinking, that a set which
>consisted of the set of natural numbers though with each terminated in an
>infinite string of zeros;-
>
>1000000000. . .
>2000000000. . .
>3000000000. . .
>etc.,
You are once again speaking nonsense; I don't know what you are trying
to say. A string of numbers which contains an infinite number of zeros
is NOT a natural number under any of the usual meanings of "natural
number". So a "natural number[...] terminated in an infinite string of
zeros" is an oxymoron.
Even trying to make sense of a such a representation doesn't lead
anywhere: how do we distinguish the string of digits representing "1"
from the string of digits representing "10", from the string of digits
represnting "100", etc?
>had the same cardinality as the set of natural numbers? And if not why not?
What you wrote is nonsense. Perhaps if you try to make it make some
sense, the question will be answerable. Right now, your questions have
no referent.
--
======================================================================
"It's not denial. I'm just very selective about
what I accept as reality."
--- Calvin ("Calvin and Hobbes")
======================================================================
Arturo Magidin
magidin@math.berkeley.edu
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