It's clear you have some math training, so I do respect you for that. But, you are confused about some of the concepts you just wrote about.

You can compare the sizes of infinities. The continuum hypothesis is a famous example.

You said real numbers between 0 and 1 are same as whole numbers between 0 and positive infinity. This is a false statement. What you meant to write is the cardinality of the set of real numbers between zero and one is the same as the cardinality of the whole numbers between zero and positive infinity. But, even when I cleaned up your statement here, it is still a false statement.

The cardinality of the real numbers between zero and one is aleph-one. The cardinality of the whole numbers between zero and positive infinity is aleph-naught. aleph-naught < aleph-one.

Yes, you can prove things with the sizes of different infinities as I have done.

You last statement apparently is an attempted slap at me, but you missed. God does not exist, so the then part of your statement is not a conclusion.

At any rate, thanks for reading me.