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I have two questions.

  1. Would you use Let $x, y$ and $z$ be real numbers. or Let $x$, $y$ and $z$ be real numbers. ? Which one is better?

  2. Would you use For $x, y\in\mathbb R$ we have ... or For $x$, $y\in\mathbb R$ we have ... ? Which one is better?

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    I would use $x$, $y$, and $z$ and $x, y \in \R$. – Manuel Apr 21 '16 at 14:35
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    I edited to use inline code, which is easyer to read in your case, but as a general comment, for your text to appear as code when you insert 4 spaces before, it also needs to be preceeded by an empty line. – Samuel Albert Apr 21 '16 at 14:35
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    I say 2nd choice: $x$, $y$ and $z$, sine it is Englishy text. I use the first choice for $f(x,y)$. – Steven B. Segletes Apr 21 '16 at 14:35
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    Regarding the first question: The second option is the correct one. In the sentence "Let x, y and z be real numbers," x, y and z fulfill the same syntactic roles as Tom, Dick and Harry do in the sentence "Let Tom, Dick and Harry be adult males." The fact that x, y and z are mathematical formulas and are entered using $ symbols is secondary. In consequence, the commas should not be included in the math-mode material. – Mico Apr 21 '16 at 14:48
5

I think you have asked several questions.

The first is about $x, y$ versus $x$, $y$. I think the second one is semantically and hence typographically right since the comma is not part of the mathematical expression. Your second example is a little ambiguous. There I would include the comma in the mathematics.

An implicit question is the choice between

Let $x$ and $y$ be real numbers

and

Let $x, y \in \mathbb{R}$

That's a question of style. I find words easier to read than symbols, but your taste may differ.

  • not 100% sure... will delete the comment. Thanks! – Rmano Apr 21 '16 at 20:06

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