I just have a small question! Really basic I'm sure but something is bothering me. Take note of the following statement:
$\forall x \in I , \exists y \in I$ such that $xy \in I $
Does this statement say that for all $x$ in $I$, there exists a $y$ in $I$ or does it say that for every single $x$ in $I$, there exists a $y$ that makes the statement true.
So for example if we took $x1$ to be $\pi$ and $x2$ to be $\sqrt 2$, can we assign them a unique $y$ for each one or for both of them?
It is a very fine difference but in proving the statement, it is rather confusing. I understand that the statement is true however but would like to solidify my reasoning.
Thank you :)
Ah yes, I understand now! Thank you everyone :) Really appreciated!