Re: Cantor Confusion

stephen@xxxxxxxxxx wrote:

Han de Bruijn <Han.deBruijn@xxxxxxxxxxxxxx> wrote:

stephen@xxxxxxxxxx wrote:

But everything can be modelled as a set.

Define "everything" and prove that claim.

By "everything", I meant everything mathematical. Of course that is not 100% precise.
And no, I cannot prove it. But so far all the various objects of mathematics can be
modelled using set theory. That is what is meant by set theory being a foundation
for mathematics. If someone were to invent something "mathematical" (whatever that may
mean exactly) that could not be described in terms of set theory, then set theory would
no longer serve as a foundation. But given that the basics such as the real numbers,
functions, limits, calculus, etc. all can be founded in set theory, it would have to
be something strange indeed. Not that there is anything wrong with strange, but you
probably would like it less than set theory.

Correction. By "everything" you probably mean "everything according to
nowadays mainstream mathematics", which _is_, of course, "mathematics",
according to your probably rather limited view. But since you can not
really prove anything of the kind, I will rest my case.

Han de Bruijn

.

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