That is ONE of about 20 different "proofs" of this fact although not a "formal" proof I'd think, however it can be formally proven as well. I believe wikipedia has a good section on this topic with several of the other proofs, although in the end I think it gets pretty involved semantically to get the formal proof, but hopefully the obvious ones will convince most people that the more involved proof is actually correct (in the end you have to realize math is not like physics or chemistry and stuff, it is simple a LANGUAGE to discuss physical phenomenon just like English or French, in the same way that the series of symbols 'c'+'a'+'t' are DEFINED to reference a specific animal species so to is .9999... = 1 DEFINED to be true).