TITLE: Infinity as an element
QUESTION [5 upvotes]: Can infinity be an element of a set? For example:
{$1,2, \infty,4$}
I understand $\infty$ is not a real number

REPLY [2 votes]: As a relevant side remark: An interesting treatment of $\infty$ is the one point compactification, for example the Riemann sphere $\mathbb{P}^1\sim \mathbb{C}\cup\{\infty \}$. This could also be done on $\mathbb{R}$ by considering $S^1$ projecting onto $\mathbb{R}$. You can google one point compactification for details.