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Can I write

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

Instead of

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

Since it is much shorter and a similar notation is usually used in sets?

Hans
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  • Better use $\forall(x,y)\in\mathbb R^2$. – Nicolas FRANCOIS Oct 27 '16 at 11:48
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    @NicolasFRANCOIS No need for that. It is well established that $\forall x,y\in A$ is just shorthand for $\forall x\in A, \forall y\in A$. – 5xum Oct 27 '16 at 11:56
  • As it is established that $\forall x\in A,\ \mathcal P(A)$ is a shorthand for $\forall x,\ (x\notin A\vee \mathcal P(A))$. :P –  Oct 27 '16 at 12:00

1 Answers1

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Yes, you can. In fact it is much more usual to write $\forall x,y\in\mathbb R$ than $\forall x\in\mathbb R\,\forall y\in\mathbb R$.

George Law
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