
Comperhension
Hello all,
I've come up with an alternative set comprehension for the former.
$\displaystyle \{\forall x : \mathbb{N}\ \ x\ /\ 2 = 0 \lor x\ /\ 3 = 0 \lor x\ /\ 5 = 0 \}\\\longleftrightarrow\\\{\ \forall x : \mathbb{N}\bullet\forall y :\{2,3,5\}\ \ x\ /\ y\ =\ 0 \bullet\ x\ \}$
Is my expression right?
Thanks very much guys!
ssharish

Re: Comperhension
First please say if this is regular mathematical notation or possibly the syntax of some computer language. Second, are the left and righthand side propositions (something true or false) or sets?

Re: Comperhension
Hi emakarov, sorry about my previous post not using the right mathematical notation or the symbols. I made a small research on what commands to use to substitute the irrelevant.
And yes its a set comprehension problem which I was trying to solve.
$\displaystyle \{\forall x : \mathbb{N}\ \ x\ /\ 2 = 0 \lor x\ /\ 3 = 0 \lor x\ /\ 5 = 0 \}\\\longleftrightarrow\\\{\ \forall x : \mathbb{N}\bullet\forall y :\{2,3,5\}\ \ x\ /\ y\ =\ 0 \bullet\ x\ \}$
Thanks a lot
ssharish

Re: Comperhension
So, these are sets, not propositions. Then the notation is {x ∈ A  P(A)} for some set A and property P, not {∀x : A  P(x)}. Also, sets can be equal: A = B; the notation A ↔ B does not make sense for sets A and B.
I would write your statement as follows:
$\displaystyle \{x\in\mathbb{N}\mid x/2=0\lor x/3=0\lor x/5=0\}=\{x\in\mathbb{N}\mid\exists y\in\{2,3,5\}\,x/y=0\}$.
Note that the righthand side uses the existential quantifier because the lefthand side uses disjunction.

Re: Comperhension
Thanks a lot for correcting me emakarov. I really quite didn't quite get that right. And also I should have put x mod y rather than x / y as '/' doesn’t provide the remainder.
Thanks very much
ssharish