1. ## Comperhension

Hello all,

I've come up with an alternative set comprehension for the former.

$\{\forall x : \mathbb{N}\ |\ x\ /\ 2 = 0 \lor x\ /\ 3 = 0 \lor x\ /\ 5 = 0 \}\\\longleftrightarrow\\\{\ \forall x : \mathbb{N}\bullet\forall y :\{2,3,5\}\ |\ x\ /\ y\ =\ 0 \bullet\ x\ \}$

Is my expression right?

Thanks very much guys!

ssharish

2. ## Re: Comperhension

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

3. ## 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.

$\{\forall x : \mathbb{N}\ |\ x\ /\ 2 = 0 \lor x\ /\ 3 = 0 \lor x\ /\ 5 = 0 \}\\\longleftrightarrow\\\{\ \forall x : \mathbb{N}\bullet\forall y :\{2,3,5\}\ |\ x\ /\ y\ =\ 0 \bullet\ x\ \}$

Thanks a lot

ssharish

4. ## 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:

$\{x\in\mathbb{N}\mid x/2=0\lor x/3=0\lor x/5=0\}=\{x\in\mathbb{N}\mid\exists y\in\{2,3,5\}\,x/y=0\}$.

Note that the right-hand side uses the existential quantifier because the left-hand side uses disjunction.

5. ## 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