Infinity is effectively just bullshit.

I’m fond of pointing out to my students that there’s a very practical reason to care about “infinity” in math:

While nothing ever reaches “infinity”, things absolutely do reach a point where they violently fly to pieces and catch on fire.

So I teach my students to substitute the phrase “explodes and catches on fire” where they see an equation that “approaches infinity”.

I find it helps them pay attention to a subject that is otherwise bullshit. Infinity itself is bullshit, but it has a place in math: telling us when to quickly duck behind a good solid oak table.