But that's like saying let's get rid of zero. You can make the argument that zero doesn't exist as equally convincingly as you can that infinity doesn't exist.

That's like saying "let's get rid of recursion".

Imagine defining a function in terms of itself! That's circular and you can always get away with just using a loop instead.

Well, it turns out recursion often works and is very useful. Just like infinity.

Saying that a function is defined "in terms of itself" is a useful mental shorthand for what's going on, but it only works if you deliberately confuse the function at compile time with the function at run time. If you think about it as a function calling itself, you don't run into this difficulty, since "calling" implies "at run time". There are a lot of things in how computer science is taught that have this "and then some magic happens; just accept it" flavor, when there's really no magic -- everything is ultimately and really imperative.

I'll repeat what I said above here:

I meant infinity, not the limit of infinity.

I have no problem with the concept of infinity in terms of limits, but that's not what this article is about. It's about the concept of infinity itself. And that is what I disagree with.