> notation in which implication means "only" I'm afraid this is a misunderstanding. What I was trying to say is that if the right-hand side of an implication d

> notation in which implication means "only" I'm afraid this is a misunderstanding. What I was trying to say is that if the right-hand side of an implication denotes a single solution, there can't be any other solution. For instance, if you write something like this: x^2 = 4 -> x = 2 this means that all solutions to "x^2 = 4" must satisfy "x = 2", which means that there can't be more than one solution. Any other solution than "2" would be a counter-example to this implication. And since there is another solution, namely "x = -2", the implication above is wrong. In other words, from "x^2 = 4" is does not necessarily follow that "x = 2". However, I agree that writing "x1" instead of "x" (as you did) kind of solves this notational issue. > Alternatively, since sqrt could be the multi valued function with no specific branch selected, this actually does give all the solutions. [...] Are you sure I was not, in fact, describing an equation in Z_2? Of course, nitpicking never stops. If sqrt() was meant to be a multi-values function, why did the formula denote "x1"? Also, was "^" ment to be "power" or "bitwise XOR"? Is "sqrt" a product of four variables? And so on. That is the whole point about admitting "nitpicking": We agree in how the formula is to be interpreted, so there is no need to get deep into formalities, as long as the real issues behind the whole stuff are clear (which they pretty much are). > Nitpicking at this level, especially if you do it often, might make you feel good about yourself, but doesn't actually get you anywhere. Correct me if I'm wrong, but this seems to be a mere ad hominem, not an actual argument. It is also a straw man, because I never claimed that this kind of nitpicking leads to somewhere. In my previous comment I was even implying quite the opposite. http://en.wikipedia.org/wiki/Ad_hominem http://en.wikipedia.org/wiki/Ad_hominem http://en.wikipedia.org/wiki/Straw_man http://en.wikipedia.org/wiki/Straw_man