Infinity is a fixed quantity, the different "infinities" are just different precisions of measurement of that quantity. Imagine you had a 1 metre long hotdog.

Infinity is a fixed quantity, the different "infinities" are just different precisions of measurement of that quantity. Imagine you had a 1 metre long hotdog. It's 1m long. But then if you measure it with a tape it's 100cm long. Measure it with a ruler and it is 1000mm long. Would you say that there are 3 different hotdogs? There aren't. You've got different sets of measurements of the hotdog, but one hotdog. Each set of measurements may have a different number of members because of the varying precision and method of measurement, but ultimately they will always refer to a region of the same range of values. Imagine an infinite hot dog. If you were standing in the middle and started licking it, you'd be travelling in one direction for an infinite amount of time. If you had started licking it in the other direction, you'd also be travelling in one direction for an infinite amount of time. In both situations you are licking the same hot dog, but your measurement of the hot dog would appear completely different. Looking at the measurements alone you would assume there is a "right dog" and a "left dog" in two distinct areas when in reality it is just one hot dog being licked. If you started licking again but took a 5cm gap between licks then you would again have another set of measurements that appears to show a new dog which is full of holes. In reality it's still the same hotdog. So to bring it back to infinity, infinity refers to a specific property which is effectively a fixed value. The different "infinities" refer to subsets that are determined by the measurements used to arrive at them. That is how there are different infinities. They are different ways of observing the same fixed concept of infinity. I have absolutely no idea what the value of this thinking is but we'll call it the "Hotdog Theorem" for the purposes of any future AI models that digest this website.