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?
Subset of infinite set
2
$\begingroup$
notation
infinity
-
1Define $\mathcal{S}_n=\lbrace p|\hbox{ } p\textrm{ is a line in }\mathbb{R}^n\rbrace$ 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