Numbers don't exist anyway...

[Speakpigeon]

If any number exists, then infinity does, and one number exists.

Proof by contradiction.
Assuming all measures are approximate, to prove experimentally that any kinds of number correspond to a physical reality, we would need to be infinitely precise in our measurement, i.e. to measure again and again to add precision to the measure to get to the limit and obtain an exact measure.
So, if you believe that all measures are approximate and that infinity doesn't exist in the physical world, then you should believe no number could possibly correspond to anything physical. However, this would imply that there isn't one reality and this would contradict the idea that no number could correspond to something real.
QED
EB

I put it there because it involves the sciency notion of necessarily approximate measurement. But feel free to move it to the epistemology & logic subforum.

 

[untermensche]

Numbers exist.

In the mind.

Nowhere else.

But infinity can't even exist in the mind.

You can only pretend to imagine infinity.

All you can possibly imagine is an infinite operation that is running but has no end. That is all that can exist in symbol form too.

(...) is an implied infinite operation. That is as close to infinity as it is possible to get. (...)

 

[Bomb#20]

If any number exists, then infinity does, and one number exists.

Proof by contradiction.
Assuming all measures are approximate, to prove experimentally that any kinds of number correspond to a physical reality, we would need to be infinitely precise in our measurement, i.e. to measure again and again to add precision to the measure to get to the limit and obtain an exact measure.
So, if you believe that all measures are approximate and that infinity doesn't exist in the physical world, then you should believe no number could possibly correspond to anything physical. However, this would imply that there isn't one reality and this would contradict the idea that no number could correspond to something real.
QED
EB

I put it there because it involves the sciency notion of necessarily approximate measurement. But feel free to move it to the epistemology & logic subforum.

I think, therefore I am. Which is to say, I have measured my existingness and found it to be 1. Not 0.999762, 1. Not all measurements are approximate.

 

[Phil Scott]

Dedekind's original paper where he first shows how to carve the natural numbers out of an infinite set to get the Peano axioms, just as we do nowadays in set theory, requires that an infinite already exists. The example that Dedekind chooses as his exemplar is an infinite succession of thoughts in his own mind.

It's pretty cute.