The discussion revolves around the logical negation of a mathematical statement involving the existence of a positive y for all positive x such that y squared equals x. Participants are exploring the implications of this statement within the context of real numbers.
The discussion is active, with various interpretations of the negation being explored. Some participants express confidence in the truth of the original statement while others are probing the conditions under which a counterexample could be considered.
There is an emphasis on the distinction between the existence of a counterexample and the truth of the original statement, particularly in the realm of real numbers. Participants are also navigating the implications of universal and existential quantifiers in their reasoning.
SammyS said:If you were looking for an example to counter this (a counter example), what would need to be true for that example ? ... and, wouldn't it take just one example (at least as regards x)?
SammyS said:If you were looking for an example to counter this (a counter example), what would need to be true for that example ? ... and, wouldn't it take just one example (at least as regards x)?
Well yes, it is true for x & y being real numbers. That doesn't mean that you can't coming up with criteria that would need to hold for a counter-example, if such existed.1MileCrash said:What do you mean counter it? I can't counter the first statement, it's true.