Re: Question: What conditions are sufficient to prove a subset does not exist?

On Jul 26, 7:57 pm, Scott <ToaTe...@xxxxxxxxx> wrote:
Arturo has stated that deriving a contradiction for any x is both
necessary and sufficient to show A does not exist. You and LuaLuna
have stated that it is not sufficient but it would be sufficient if
you proof S does not exist.

In the general case, if you can derive a contradiction from the
assumption that A exists, that is sufficient to show A does not exist.

What you must clarify is what assumptions you have used in the
derivation of the contradiction. If the existence of A is your sole
assumption, then A does not exist. But in your case the existence of A
depends on the existence of f in such a way that if f exists, A has to
exist.

So, in this case, it is the existence of f what you must reject.

Regards

.

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