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I do not know what it is.

$\mathbb{R}$ is the set of real numbers.

How come $\mathbb{R}\times\mathbb{R}\times \ldots $?

Thanks.

Chris Brooks
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Ribz
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1 Answers1

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It's the set of all functions $\mathbb R\rightarrow\mathbb R$. In general $X^Y$ is the set of all functions $Y\rightarrow X$.

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    Thanks. So it is a simple notation. I was confused with $\mathbb{R}^n$ – Ribz Apr 14 '14 at 18:19
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    @det You should think of it as a straight generalization of this notation. A function from from $Y$ to $X$ can be thought of as a "tuple" of length $Y$, all of whose entries are elements of $X$. – Andrés E. Caicedo Apr 14 '14 at 18:22
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    @det: $\mathbf{R}^n$ can be thought of as the same way; if you interpret it as a von Neumann ordinal $n = { 0, 1, \ldots, n-1 }$. –  Apr 14 '14 at 18:22
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    Yes got it. Thank you all very much. – Ribz Apr 14 '14 at 18:25