The complete wave function of your room contains some elephant-like fluctuations in the distant decimal places.
https://en.wikipedia.org/wiki/Boltzmann_brain
I'm not sure if a functioning elephant is more or less likely to be honest....
There's something about nihilism. It's being a self defeating argument, but educating. Then there's constructivism in various senses.
There's something about finitism, too, computable numbers and what not. Infinity is rather ... monotonous.
If you're going to look at more than just integers, infinity is everywhere, in between every number you can count, and then some! 0 is as meaningless but so is every other number!
If you limit to integers or even just whole numbers, 0 is meaningful, just like all the numbers...