(adsbygoogle = window.adsbygoogle || []).push({}); How "big" is this number?

I have had absolutely no sleep for a while, so my math brain has been failing me. Last night, I was working on a problem and I believe that one of my connections is wrong. Is this number countably infinite or uncountably infinite (asmapproaches infinity):

[itex]\sum_{n=1}^{m}{(\frac{m!}{n!})^{a}}[/itex]

I feel like it is countably infinite, but I am not sure.

Also, what about just simply (m!)^{a}as m approaches infinity? If it is uncountable, that will be rather cool, too, as that is what one of my proofs hinge on.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# How big is this number?

**Physics Forums | Science Articles, Homework Help, Discussion**