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Let's say I have defined $X$ = users type x and $Y$ = users type y, and I would like to define $u$ is element-of $X$ and also element of $Y$, is there a simpler way to express, or the expression below is in the simplest form?

$$u =\{ e | e \in X \wedge e \in Y \} $$

Thank you.

Regards, Andy.

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up vote 4 down vote accepted

You can say that $u = X \cap Y$. This should be the easiest standard way to use set notation to denote this.

Hope that helps,

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so there is no such thing as {$e \in X,Y$} I supposed? – cherhan Dec 5 '11 at 5:19
@cherhan I think most people would find that ambiguous. – Dylan Moreland Dec 5 '11 at 5:20
It is not very convenient to use $\{ e \in X,Y \}$ is mathematics since the need to use the notation you suggested doesn't show up, the notation $X \cap Y$ is more suggestive and more compact, too. – Patrick Da Silva Dec 5 '11 at 5:21
Yes that sounds good, I will begin with some discrete maths reading and move on from there, thanks! – cherhan Dec 5 '11 at 5:37
When dealing with sets, it is customary to use capital letters for sets and lowercase letters for elements. So, if you want to denote the set of all elements that are members of both $X$ and $Y$, then $U = X \cap Y$ is more typical. If you mean to simply denote a single element that happens to belong to both $X$ and $Y$, then you would say $u \in X \cap Y$ (the $\in$ means "element of"). – Austin Mohr Dec 5 '11 at 8:14

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