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I was looking around on the internet ( as one does) and found the expression $$2^{\mathbb {R}}$$ To me this reads as 2 two the power of the real numbers. But what does that mean? Does it mean the set of all $2^x$ where $x$ is a real number?

Nash J.
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Mark S
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  • The set of all mappings from $\mathbb R$ to ${0,1}$, maybe? – Oscar Lanzi Dec 28 '19 at 20:19
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    If $A$ is a set, then $2^A$ usually means the set of all subsets of $A$. This is the same as Oscar Lanzi's comment, by the way. – B. Goddard Dec 28 '19 at 20:21
  • But it can also be ${2^x | x \in \mathbb{R}}$, i.e. the set of all numbers of the form $2^x$ for some $x \in \mathbb{R}$, as you noted it. – Botond Dec 28 '19 at 20:23

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It usually denotes the set of all subsets of $\mathbb{R}.$ This is almost certainly the case here, but you've provided no explicit context.

kodlu
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