Pythagoras

So we all know that to find the length of a hypotenuse you use the formula A squared + B squared = C squared.  What happens, however, if A and B = 1 ?  Did Pythagoras note this problem?  Is 2 the only number with an infinite decimal for a square root?  How do you find the length of the hypotenuse in this situation?  

>>23
"There exist elements with property P"

"There exist elements with property P, and they are precisely the elements with property Q"

This is NOT A FUCKING GENERALIZATION. Not mathematically, not colloquially. I'm not saying it is any less general: it simply restates the first with more specificity. You don't generalize something by turning an existence statement into a classification statement. A generalization would be something like:

"There exist elements satisfying property R(n) for any relevant n, and for some value of n, R(n) is equivalent to P"

In this case, for instance, a generalization would be "There exist natural numbers with irrational n-th roots for any natural number n > 1." Then, in the case n = 2, we see that there exist natural numbers with irrational square roots.