3^0=1 and 4^0=1 can't both be true using your argument Just like any number raised to the 0 is 1, 1 plus any number is 3 I can prove this like this; Well, if you want an actual formal proof, see the metamath proof of 22=4 (11=2 is boring because that's how it defines 2) (11=2 is boring because that's how it defines 2)The later theorem alluded to, that $11=2$, appears in section $\ast102$, considerably farther on I wrote a blog articlea few years ago that discusses this in
Prove 0 1 Using Calculus Integration By Parts Mind Your Decisions