[zeebeecee]

Do integers exist? Do sequences of integers exist? If they do, so do the real numbers.

This is because any positive real number has a decimal expansion which determines it. For example pi = 3.1415926535... or 1/3 = 0.3333333...

[magneticnorth]

Do infinite sequences of integers exist? Especially all the ones that can't be compressed into a finite description? I don't think that's clear at all.