Re: OT: mathematicians (Was: Re: Results of Poll by Email No. 27)

On Tue, 8 Apr 2003 11:32:44 -0400, H. S. Teoh <hsteoh@...>
wrote:

>On Tue, Apr 08, 2003 at 11:26:51PM +1000, Tristan wrote:
>
>And even the idea of sets itself would be overly complex (mathematically
>speaking) if we allowed sets of arbitrary objects; therefore in formal
set
>theory, sets don't contain anything except other sets. By the same
>argument, the only relational operation on sets is the "contains"
>relation.  The most basic assumption of set theory (axiom #1) is that at
>least one set exists. This is usually understood to mean the empty set.
>
>Putting these together, you can think of 0 as the empty set, 1 as the set
>that contains the empty set, 2 as the set containing the 0 and 1 (i.e.,
>the empty set and the set that contains the empty set), ad infinitum. In
>other words, the entire field of mathematics is made of empty sets; all
>theorems are ultimately just pronouncements about empty sets. Now we know
>where mathematicians dispose their cups after consuming all that
>coffee.[2]
>
>:-P
>
It hardly seems complete. What is -1? The largest set contained by the
empty set? I didn't think mathematicians would like a system that couldn't
be extrapolated to a more general number space.

```sii``s``s`ksk`ki

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