I have a question about the use of infinity and geometric sets. Say I am trying to graph an equation, and the result is all values greater than or equal to, say, $3$. From what I've seen, the proper way to write this is $(\infty, 3]$, where $3$ is included, as expected, but infinity isn't. Why?
I realize $\infty$ is obviously infinite, and therefore this is hard to imagine, but wouldn't $\infty$ then be included. Otherwise, it seems like the value would NOT include $\infty$.
I can kind of understand, as $\infty-x$ is still infinity. But therefore, should infinity ALWAYS be included? This is a real head-scractcher.