Ironically, finitists and constructivists don't like proof by contradiction...

I agree though, that you have come up with a contradiction. Specifically, because you seem to believe these two statements:

There are finitely many natural numbers.

Given any finite list of natural numbers, we can always produce another natural number not on that list.

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moi2388 5 days ago | parent [-]

Leading to yet another finite list. You will never actually end up with an infinity. You’ll run out of space, you’ll run out of time.

It “exists” just like magic in Harry Potter exists. Not really.

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griffzhowl 4 days ago | parent [-]

No one thinks you can actually write an infinite list.

What it means for there to be infinitely many natural numbers is that for any finite list, there are natural numbers not on that list (something you appear to agree with). If there were finitely many natural numbers this wouldn't be true

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moi2388 4 days ago | parent [-]

Sure they do. Cantors argument, infinite sums, mathematicians keep using infinite lists as if they do exist.

Let’s not even begin about the axiom of choice. Or transcendental numbers.

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griffzhowl 3 days ago | parent [-]

You're also treating the natural numbers as infinite if you think there can't be a finite list containing all of them

	▲	moi2388 2 days ago \| parent [-]
		Depends. Not the way I look at them. But this discussion is getting off topic (my own fault), so perhaps we should continue it somewhere else.