In mathematics education, I always disliked the way inifinity is shoehorned into the different sets of numbers and treated as "just another number", so that you can write shorthands like: 1/∞=0, instead of the more accurate ∀ε>0, ∃c>0: x>c ⇒ 1/x<ε

Infinity is not a number. It's a limit.

Treating it as a number only confuses real understanding of it.