| 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.
How am I misguided about what a proof is? I'm the one suggesting this type of variable declaration manipulation is utter nonsense. There is no equation to solve, only an assertion that x is 2, or in the OP case that x = 0.999...
| Soleron said: His explanation doesn't contain any invalid steps. Yours does. Neither are formal proofs but no one here would understand the formal proof. |
Mine does not contain invalid steps because there is no rule that describes variable declaration manipulation.
You are missing the fundamental point here, which is that it isn't an equation. X is already known, any other value you associate to x is invalid by this very reason, which is why logic goes out the window.
I'm sure many people can understand a formal proof here.
