Four types of infinity
1) Precision infinity - You will never be able to precisely measure anything in quantitative terms. You will have to accept some level of imperfection and trucation, the goal is to minimize it as much as possible
2) Misunderstood infinity - An equation that produces an infinite quantity due to incompleteness
3) Massive infinity - A number so large, we will never grasp the size. While a true infinity is forever and impossible to quantify, there are numbers so large we consider them infinites for practical terms. Such as procedural reasons.
4) Miniscule infinity - cut an item down by half, repeat and keep going. It can only keep going down further with no ending. There is a concept of Plank length which is the smallest possible unit of existance in the universe we know of, that wouldn't quickly collapse into a mini black hole and vaporize into radiation. But as we know, our understanding ends there.
We can go onto some weird voodoo infinities, but these are the ones I'm aware of