OK, so let’s take some steps back here.

You said that the cardinality of integers and real numbers are not comparable. But here https://en.wikipedia.org/wiki/Cardinality#:~:text=In%20mathematics%2C%20the%20cardinality%20of,has%20a%20cardinality%20of%203.

the cardinality of integers and real numbers is compared with a result of |N| < |R|. Where exactly is the error there? I mean exactly, not some imprecise/error prone reasoning. Go to the wiki and tell me the line where they are wrong.

Besides: you state that one cannot add or subtract anything to infinity because it is not a number. I am going to falsify this sentence by doing a subtraction of 2 infinities: ∞ - ∞

• Lim (x) for x->∞ = ∞
• Lim (x+1) for x->∞ = ∞
• Lim (x+1 -x) for x->∞ = 1

Just subtracted two “infinites” in the right way and got 1 as result.

I therefore conclude that your argument is wrong and Cantor is right.

By the way, the reason that we say infinity is a concept and not a number is because if you write ∞ - ∞ = ? you don’t have enough information to tell anything. But, for example, if you keep the information on how 2 functions go to infinity, than you can compare them.

Same reasoning for cardinality.