Infinity does exist a priori and independent of proof though.
It's like our natural rights. We don't need to prove that they exist. They simply exist because we reason about them.
Discussion
Not necessarily. I came to these conclusions when thinking deeply about simulation.
It would require infinite energy to simulate truly analog data with digital computation. So if we can prove something is truly analog, or continuously variable, then we can prove that we do not live in a digitally computed simulation. The issue I found is that science literally cannot prove with 100% certainty that something is continuously variable or infinite in any way. It can only prove something doesn’t end within the bounds of the test. Thus, I remain unsure of whether we live in “base reality” or not.
I agree that it’s useless to live as if infinity doesn’t exist. Whether we have true infinities or illusions of infinities makes little difference in life. I’ll conclude by saying that I have faith that infinity is real. This has greatly strengthened my faith in God.
My point is, there are scientific truths that do not require proofs in order to be true.
You can simply arrive at them through your reasoning faculties and know it to be true absent of evidence.
The concept of infinity is one of them.
P.S. Since your handle's name and picture refer to anarcho-capitalism, I'll leave you with a book recommendation that is a wonderful read for anyone who loves both science and liberty:
https://mises.org/library/book/economic-science-and-austrian-method