You are confusing yourself again because you are talking about "how many" elements there are in infinite sets, or "twice as many" elements in an infinite set as in another. Drop that language, and you'll be all right. It doesn't make any more sense than saying that there is twice as much liquid in this empty glass as there is in that other empty glass. It's true though, because 2 times zero is still zero, just the same as two times infinity is still infinity. It's true, but it's just not a useful statement to make. Multiply zero by 5 and it's still the same zero, so why bother multiplying it? Multipy infinity by 10 and it's still the same infinity. Raise zero to the square, it's still the same zero. Raise infinity to the square and it's still the same infinity. Doing any of that to the infinite size of an infinite set does not change its cardinality.
The trick to get it is to forget entirely the conventional notion of size. Pretend you never learned what size was, or never knew how to count elements in a set. Replace it entirely with the notion of cardinality and the existence of bijective/injective functions between a set and some reference set. That is actually what you subconsciously do when you say there are 3 elements in the set {a,b,c}, what you really do when counting the elements is creating a bijection between this set and the reference set {1,2,3}. Work from this premise, and the rest will come naturally.
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