It seems to me that you are doing the mistake that you are attributing to Cantor.

"To say that one is “bigger” than another is to say that you can add at least one to infinity. This is not possible, as infinity is an absolute to start with."You just treated "Infinity" as a number! You want to add 1 to a concept (infinity) and conclude that it is absurd.

I state that n < n +1 for every n in the set of integers. So I "added one to infinity". But I did in the proper way: I described a property that is valid for every element of the set, which has infinite items.

On the contrary, you are confusing "Infinite" with a number and conclude "This is not possible, as infinity is an absolute to start with".So you squash and blender sets of infinite number of items into this "Infinity" number of yours that is the same for every imaginable set.

Since you can create an injective map between integers and real numbers, but you cannot create an injective map between real numbers and integers, it make sense to me that real numbers are "bigger in size" than integer numbers. Than we have to define this "size" or cardinality properly. But I think this was out of the scope of the Marc Barroso article.