Which one of these statements is true? $$ \exists y >0 : \forall x > 0, y < x $$ or $$ \forall x > 0 \exists y > 0 : y < x $$ I think the second statement is correct, since for all x greater than 0, there exists at least one value of y > 0 such that y <x. The first statement doesn't really make a lot of sense, there exists at least one value of y >0 such that for all x >0, y < x. What this says to me is that there are values of y which are less than all the values of x > 0. which cant be true since that would imply $$ y \le 0 $$ Could someone tell my why i am correct, or why i am wrong. Please!