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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.

1 Answers 1

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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?2011-12-05
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    @cherhan I think most people would find that ambiguous.2011-12-05
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    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.2011-12-05
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    DylanMoreland: agree, @PatrickDaSilva:thanks. A bit newbie to mathematical notation and formalisation from a coder background. I was wondering is there any books on such topics or good material to learn?2011-12-05
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    What do you have in mind? Do you need to learn anything specific? Your question is rather vague, if you just "want to learn maths", there are plenty of ways you can go.2011-12-05
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    @PatrickDaSilva: No, I am particularly interested in mathematical notation and formalisation of algorithm (please let me know if it's still too vague)2011-12-05
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    Hm. Mathematical notation can be found in probably any book speaking of mathematics at the beginning, but if you wanna learn how to understand it and play with it, maybe you are looking for a introductory course in discrete mathematics, to learn to play with logic in maths, sequences and recursion (called *induction* also in mathematics). Does that sound like what you're looking for?2011-12-05
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    Yes that sounds good, I will begin with some discrete maths reading and move on from there, thanks!2011-12-05
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    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").2011-12-05