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if \(f\) is identically zero there is nothing to prove

Well you are proving backwards you gotta start from the beginning

i guess we have to worry about \(f\) being continuous
start by showing \(f(0)=1\)

Not exactly sure hmmmmm

\[f(x)=f(x+0)=f(x)f(0)\implies f(0)=1\]

Aha I see that

Thanks :) Just gonna string some stuff together here :)

Ohhh I like thisssss :)