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0 pointsCJefferson7mo ago0 comments

I don't agree, but I agree it's an interesting discussion to have.

When is the set of all possible subsets of natural numbers worth considering more than the set of all sets which don't contain themselves (which gets us Russell's paradox of course), once we start building infinite sets non-constructively?

The naturals to me are a clearly separate category, as I can easily write down an algorithm which will make any natural number given enough time. But then, I'm a constructionist at heart, so I would like that.

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kcexn7mo ago

You can construct a real number by using an infinite series so it's no less constructive than a rational function on the naturals.

Non-constructive arguments are things like proof by contradiction i.e., the absence of the negative implies the existence of the positive.

CJeffersonOP7mo ago

Except we can only describe those infinite series for a countably infinite number of the reals, so there are all these reals expressed by infinite series we don’t have any way to describe. Why do we need those ones? (To be clear, I realise this isn’t the current standard opinion of most mathematicians, I choose to be annoying).

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