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Math Help - Notation

  1. #1
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    Notation

    I am trying to say: Every a in A is in B

    Is the following notation correct?

    [(universal quantifier) a (epsilon) A] (epsilon) B
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  2. #2
    MHF Contributor undefined's Avatar
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    Quote Originally Posted by Noxide View Post
    I am trying to say: Every a in A is in B

    Is the following notation correct?

    [(universal quantifier) a (epsilon) A] (epsilon) B
    I could be wrong but I think what you wrote would not be considered correct use of notation.

    I would instead write:

    \forall\ a \in A: a \in B

    I believe this has the same meaning:

    a \in A \Longrightarrow a \in B
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  3. #3
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    Quote Originally Posted by undefined View Post
    I could be wrong but I think what you wrote would not be considered correct use of notation.

    I would instead write:

    \forall\ a \in A: a \in B

    I believe this has the same meaning:

    a \in A \Longrightarrow a \in B


    \forall\ a \in A: a \in B

    does ":" mean such that?

    If you're interested I'm just talking about the case where A is a subset of B
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  4. #4
    MHF Contributor undefined's Avatar
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    Quote Originally Posted by Noxide View Post
    \forall\ a \in A: a \in B

    does ":" mean such that?

    If you're interested I'm just talking about the case where A is a subset of B
    You could read ":" aloud by simply pausing: "For all a in A, a in B." Or you could read it as "it is true that."

    Here's another way.

    A \subseteq B if and only if \forall x(x\in A \Rightarrow x\in B)

    Edit: upon reflection, what I wrote above:

    Quote Originally Posted by undefined View Post
    I believe this has the same meaning:

    a \in A \Longrightarrow a \in B
    isn't precise enough, because a is unspecified, thus the expression is not a sentence/proposition in the language (it cannot be assigned a truth value); we would still need the \forall symbol, like I did in this post.
    Last edited by undefined; June 4th 2010 at 12:50 PM.
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