A user on Math.Stackexchange asks
How would you prove that !!2^{50} < 3^{33}!! without directly calculating
the values
My mathematically impeccable shitpost reply:
The methods given in the other answers are all very
complicated. Furthermore,
as Did points out in a comment
they all depend on facts which are not in principle any less complex
than the statement that is to be proved. The following method is
quite simple and satisfies the request with no advanced theory
whatever and “without calculating the values” as required:
Take a
heap of red beans of size !!2^{50}!! and a heap of navy beans of
size !!3^{33}!!. Repeatedly remove one bean from each pile until the red
pile is exhausted. At that point some navy beans will remain and the
claim is proved.
Do I want to suggest that there is a deep and subtle point lurking
here? No, I better not push my luck.
