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Math Help - Comperhension

  1. #1
    Junior Member
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    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
    Last edited by ssharish; October 20th 2011 at 03:46 AM. Reason: To make nesscary changes to use the right mathematical symbols
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  2. #2
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    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?
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  3. #3
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    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
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  4. #4
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    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.
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  5. #5
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    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
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