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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 can't be true since that would imply $$ y \le 0 $$
Could someone tell my why i am correct, or why i am wrong. Please!
$$ \exists y >0 : \forall x > 0, y < x $$
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 can't be true since that would imply $$ y \le 0 $$
Could someone tell my why i am correct, or why i am wrong. Please!