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That's not how infinity works, which is why many results involving infinity are counterintuitive.

For instance, consider the natural numbers and just the even natural numbers. Intuition says these two sets must differ in size, because I took one set and removed half of its elements. But the mapping f(x) = 2x is a trivial bijection from the natural numbers to the even natural numbers, showing the two sets are of equal size.

Do you agree with the statement that two infinite sets are of different cardinality if it can be shown that no bijection exists between them? Let's consider an uncountable set that's simpler to imagine than the real numbers: the power set of the natural numbers, that is, the set of all subsets of N. It can be shown that no bijection exists between any set and its power set (Cantor's theorem [1]). Do you agree with that theorem? It can also be shown that a bijection does exist between the power set of N and R [2], implying they are of the same cardinality, and are both of a larger cardinality than N.

> There is only one infinity. It means "repeat".

Then what does it mean to you that infinite sets can be constructed that can be shown to have no bijection between them?

[1] https://en.wikipedia.org/wiki/Cantor%27s_theorem

[2] https://en.wikipedia.org/wiki/Schr%C3%B6der%E2%80%93Bernstei...