[db48x]

That's not a very good assumption; the universe has a finite size and therefore cannot contain an infinite amount of information.

[szemet]

If the universe cannot contain infinite amount of information then it follows that there are infinite knowledge we cannot know - simply because we cannot store it anywhere (in brains or computers or anywhere).

For example: exact prime factorization of all natural numbers, etc...

Of course this is true only if you accept induction. So you can still back off by declaring yourself finitist* ;)

* https://en.wikipedia.org/wiki/Finitism

[jsprogrammer]

The observable universe appears to have finite size. I don't know how you could prove it though.

[nitrogen]

The observable universe is effectively defined to be finite in size. The proof comes from the speed of light.

[jcoffland]

Assuming a big bang is the source of all matter. Our observable universe may only be a spec in something much larger with out violating any of our "laws" of physics.

[jcoffland]

Assuming the observable universe is everything there is is not a good assumption.