I had a question about mapping, for example: what do they mean by $R \times R \to R$? is that not just $R \to R$?
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$\times$ is the Cartesian product. – Mar 02 '16 at 02:45
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What does that mean exactly? – genieSessions Mar 02 '16 at 02:51
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https://en.wikipedia.org/wiki/Cartesian_product – Mar 02 '16 at 02:57
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When we write $f: \mathbb{R} \times \mathbb{R} \to \mathbb{R}$ we mean that $f$ takes pairs $(x,y)$ to $\mathbb{R}$ where $x,y \in \mathbb{R}$. For example, consider the map $f(x,y) = x$ then $f:\mathbb{R} \times \mathbb{R} \to \mathbb{R}$.
Faraad Armwood
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Yup, its just a indicator which tells you what space each entry comes from. By convention we write $\underbrace{\mathbb{R} \times \cdots \times \mathbb{R}}_{n \ \textrm{times}} = \mathbb{R}^n$ because writing it out all the time would be painful. – Faraad Armwood Mar 02 '16 at 03:09