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Topic: Matheology § 175
Replies: 3   Last Post: Dec 10, 2012 1:54 PM

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Michael Stemper

Posts: 671
Registered: 6/26/08
Re: Matheology � 175
Posted: Dec 10, 2012 1:54 PM
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In article <ka5442$7no$1@news.albasani.net>, "nofingers" <invalid@invalid.com> writes:
>"WM" <mueckenh@rz.fh-augsburg.de> wrote in message news:19e8bf9c-e0e0-40a2-a259-2c4185e1aa55@r6g2000yqd.googlegroups.com...

>>Until then, no one envisioned the possibility that infinities come in
>>different sizes, and moreover, mathematicians had no use for “actual
>>infinity.”


Fortunately, we don't stand still on the inherited wisdom of a bunch of
dead guys. Rather, human ingenuity constantly broadens our horizons.

>> The arguments using infinity, including the Differential
>>Calculus of Newton and Leibniz, do not require the use of infinite
>>sets.

>
>that is wrong.


Off-hand, I'm not sure how one could prove the FTC otherwise.

>>There are only countably many names.
>
>Wrong. a name is simply a set of letters of any number.


WM appears to have gotten something rigth.

The set of names, as you defined them, is a countable set. Taking
English and the Latin alphabet as an example, we can view each string
as a base-26 encoding of a natural number:
a = 1
b = 2
...
z = 26
aa = 27
ab = 28
az = 52
...

So, the set of all possible finite strings can be put in bijection with
the naturals. Therefore, this set is countable.

Since not all of these strings are English words, words are a proper subset
of this, and hence countable.

--
Michael F. Stemper
#include <Standard_Disclaimer>
Build a man a fire, and you warm him for a day. Set him on fire,
and you warm him for a lifetime.




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