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Correctly. Just do not transfer, but project. For example, real space is in one – to-one correspondence with the set of real numbers; past time is in one-to-one correspondence with the countable set of rational numbers, and so on. The problem is that many scientists refuse to do this for reasons far removed from philosophy.
I don't think so, because infinity is a conditional sign, roughly like time, but a little different. Infinity is a constantly increasing quantity and if we (according to my logic) transfer it to our world, then something will constantly increase in quantity and gradually it will fill the entire space.
Mathematics is a description of our world. Rational values provide insight into the mechanics of our measurement limited by our capabilities. But in reality, our existence is an irrational concept. For example, we are made up of matter, matter is made up of molecules, molecules are made up of atoms, atoms are made up of quarks, and on and on theoretically you can reach strings, but we rest on the fact that we are made up of nothing. In mathematics, this is 0, but we describe our existence as 1 and this distance between 0 and 1 is infinity, which is nothing more than an integral part of the real world.