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What does $\mathbb{R}∗\mathbb{R}$ mean? I'm sure this has been asked before, but I do not know how to search for notations in past questions.

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    I have never seen that before. Possibly the same as $\mathbb{R}\times\mathbb{R}$ as $*$ is sometimes used to denote multiplication in other settings, but that's just a guess.2011-12-28
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    Could you tell us more about the context where you saw this notation?2011-12-28
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    May be a free product2011-12-28
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    I was reading the this section of StackExchange, and saw something that said $f: \mathbb{Z} * \mathbb{Z} \rightarrow \mathbb{Z} \times \mathbb{Z}$.2011-12-28
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    Thinking back, I think Norbert is right. I'm pretty sure I've seen this used for either free product or abelian free product.2011-12-28

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