0.9999.... = 1.0

[ebw]

dsgrue3 said:

ebw said:

You are deeply misguided about what a proof is.  Your calculation begins with the premise that x=2 and deduces that x = ±2, which I completely agree with.  You seem to misunderstand what the ± notation means.  The last sentence reads "x must be either 2 or -2", which of course it is, since we happen to know it is 2.  There is nothing in the sentence "x = ±2" that says that x could be -2, only that x cannot take any other value.  Likewise, Pezus's example seeks to show that if x has any value whatsoever, it must be 1.  Reading this as "-2 = 2" is utter nonsense.

Actually +/- means either one is a solution for x, which it obviously isn't.

No, that is exactly what ± does not mean, as I have already stated.  Your interpretation leads to fuzzy logic, while the standard interpretation is really quite consistent.  Your bald assertion amounts to "I choose to interpret this statement in this non-standard way so as to criticise the logic which is only flawed by my invalid interpretation".