Ok, just as long as you weren't confused into thinking you had an alternate proof 😅
Feel like such an akchually guy right now, but wasn't 100% sure.
Mentioned it before, but this interview covers a ton of the deep but not too-advanced math stuff, in particular the beginning section covers all this infinity stuff. Linking it, just in case :)
https://youtu.be/14OPT6CcsH4