Infinity cannot exist in any form, or there be basically no room for anything else in this universe (save the infinite thingie) certainly no room for the kittys two to hog more than there fair share of my bed.
That rather depends. In maths infinity in commonly used in, for example, calculus, set theory and fractals. As maths is theoretical, so the use of ∞ is perfectly valid as a thoretical concept. Then again, because I am an INTJ in MBTI theory does not necessarily entail a universal truthfulness, per se, regarding the term INTJ. (But then again there's theories and there's theories.)
Let me illustrate. Say you wanted to accomodate an infinite number of pussies in your bed comfortably... You have a scheme where each pussy has a little bed; as soon as a new pussy arrives, all the pussies move one along. Providing you add a bed every time a new pussy arrives, you have a countably infinite number of beds (and pussies). Aren't you a lucky boy.
In cartography, you may be asked to measure a coastline of, say, the UK. If you want, you can use the idea of the perimeter of a snowflake, to illustrate what happens as you enlarge the scale of your map from 1:50,000, 1:25,000, 1:10,000 and so on until you pass 1:1...
You might eventually conclude that you have been given an impossible task as infinity is not countable, unlike your home, which has a countably infinite number of little beds, each with a purring cat.
In other words the term is open to equivocation.
Meaow.