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A point. There is an infinite number of lines intersecting it, but this is less than the number of possible lines. How do we represent this in mathematical notation?

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    Define $\mathcal{S}_n=\lbrace p|\hbox{ } p\textrm{ is a line in }\mathbb{R}^n\rbrace$ and for $x\in\mathbb{R}^n$, $n\geq2$ define $\mathcal{S}_n^x=\lbrace p|\hbox{ } p\textrm{ is a line in }\mathbb{R}^n\textrm{ passing through }x\rbrace$. Then $\mathcal{S}_n^x$ is a proper subset of $\mathcal{S}_n$, in symbols: $\mathcal{S}_n^x\subset\mathcal{S}_n$ or $\mathcal{S}_n^x\subsetneq\mathcal{S}_n$ (to avoid confusing it with not-necessarily-proper inclusion). Is this what you want to express?2012-01-31

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