Re: Cantor Confusion

Han de Bruijn wrote:
Lester Zick wrote:

On Thu, 7 Dec 2006 03:00:21 -0500, David Marcus
<DavidMarcus@xxxxxxxxxxxxxx> wrote:

If you use ZFC (or something similar) as your foundation for
mathematics, then everything is a set. Of course, while solid
foundations are good to have, if you are living on an upper floor, you
may prefer to ignore what is going on in the basement.

So you're saying that set "theory" is all of mathematics? Of course
since what you say isn't necessarily true that's not exactly a ringing
endorsement of set "theory".

It's quite simple. Set Theory can not be the foundation for mathematics,
because NOT EVERYTHING IS A SET. E.g. a calculation is mathematics, but
it's not a set.

But calculations performed on the real numbers can, in principle, be
translated to operations on sets and back again to obtain identical
results.

Of course, we might disagree whether something is mathematics, just as
we might disagree over whether something is an example of Italian
cooking. Can you give an example of something you consider mathematical
that you feel cannot be modeled using sets as described by ZFC?

Set theory may be of limited use, but it's supremacy is
complete nonsense, and will be overruled in time.

"Supremacy"? It's not somehow "better" than other branches of
mathematics. The fact that in principle we can perform calculations
equivalently by performing certain set theoretic operations doesn't
mean that the latter is a "good" way of performing calculations.

Set theory is primarily a tool used to unify different branches of
mathematics by providing these different branches with a common
language.

Cheers - Chas

.

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