> The definition is that sqrt(x²) = x, which has positive and negative solutions in x for any x² > 0. When people write "sqrt", they mean the function, or, "pr

> The definition is that sqrt(x²) = x, which has positive and negative solutions in x for any x² > 0. When people write "sqrt", they mean the function, or, "principal square root". "A square root" is a different thing. Saying "the definition" makes sense only within the context where the definition is established, otherwise we have to fallback to the common usage. Wittgenstein would laugh at this conversation. Also, I'm not arguing for this convention ("it needs to have a single formula to be a function"). And when you start substituting symbols, almost nothing withstands this test. Because then you can always always twist the formula into several cases. And generally thinking about functions as something that is defined by formulas is a very limiting view. Almost all functions cannot be defined by formulas.