Definite or indefinite article for non-singletons?

[Michael F. Stemper]

On 27/07/2019 17.43, Stefan Ram wrote:
> Terry Reedy <tjreedy at udel.edu> writes:
>> In mathematics, *every* set is 'the'.

This is correct, at least in ZF, where the Axiom of Extensionality says
that (in English) if A and B have exactly the same elements, they are
the same set.

> |Example 2   Let T be an non-empty set and ...
> [PDF] Real Analysis on Metric Spaces - Columbia University

It's obvious that "an" is a typo, either for "any" or "a". Assume for
the sake of argument that it's intended to be "a", as in "Let T be a
non-empty set..." T is indeed "a" set, but it's the only set that has
the same elements as T. Therefore, once you've let T be some specific
non-empty set, it is *the* set T.


-- 
Michael F. Stemper
Life's too important to take seriously.