Re: Humble pie.

From: Arturo Magidin (magidin_at_math.berkeley.edu)
Date: 06/28/04 

Date: Mon, 28 Jun 2004 22:20:24 +0000 (UTC)

In article <D1yDc.279$9t5.92@newsfe1-win>,
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.
>
>I agree, there is no natural number terminated in an infinite string of
>zero's.
>What I am describing is a completely different set. One in which each
>element is a unique infinite string formed from a single natural number
>followed by an infinite string of zeros - and every natural number is used
>as the basis to form one and only one infinite string belonging to the set.
>Each member of this set obviously can not be described as a natural number..

What you have described does NOT constitute a "unique infinite string"
for each natural number. Everything else is moot at this point.

>> 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?
>>
>
>You are right, I should have specified that the natural number component be
>in binary form.

This does not solve the problem! "10" is a perfectly fine binary
form. So is "100". You've not solved the problem of figuring out what
number corresponds to a representation. Your "unique representations"
have an infinite number of natural numbers corresponding to the same
(infinite) sequence of digits.

>>
>> >had the same cardinality as the set of natural numbers? And if not why
>not?
>
>Does the set I describe have the same cardinality as the set of natural
>numbers, and if not why not?

You have not described a set correctly enough to figure out just what
it is you are talking about. You claim that each natural number gets a
unique representation, but this is not the case: multiple numbers get
the same representation. Just what is it that you are trying to do,
anyway?

Any questions relating to the scheme you describe are moot, because
the scheme simply does not have the properties you assert it should
have.

>> 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.
>>
>
>Hope that makes more sense to you.

It makes perfect sense: you don't know what you are talking about. 

-- 
======================================================================
"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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