From my course text:
If the universe of discourse is composed of the natural numbers then we can write:
∀X (odd(X) ⇒ (∃Y (X = 2 x Y)))
If the universe of discourse is everything then we can write:
∀X ∃Y(odd(X) ⇒ (X = 2 x Y))
I know that the difference is the position of the "∃Y". But I do not understand why this occurs. Can someone explain to me why "∃Y" needs to be shifted to the front?
Thanks!