I don't know why you think I'm worried about confusing programmers? Did I say that?
My claim is that all of the results you are attributing to "infinity" are true for other reasons, like diagonalisation, and cannot be proven directly from the concept of infinity like you are claiming. It's a heuristic that is not helpful for actually doing the mathematics.
Feel free to prove me wrong by giving me a (mathematical, not hand waving) proof of the halting theorem that only makes use of "infinity" as you are describing it. You won't be able to do it, because it's not the crux of the halting problem. It holds for infinite programs too, because diagonalization arguments don't care how big your set is.
Anyway, I don't really have the energy for this. I appreciate the time and discussion, for which I thank you. But as someone who studied maths at a PhD level and now programs for a living, I'm not getting much out of these ideas. Perhaps we can just agree to disagree for now.
My claim is that all of the results you are attributing to "infinity" are true for other reasons, like diagonalisation, and cannot be proven directly from the concept of infinity like you are claiming. It's a heuristic that is not helpful for actually doing the mathematics.
Feel free to prove me wrong by giving me a (mathematical, not hand waving) proof of the halting theorem that only makes use of "infinity" as you are describing it. You won't be able to do it, because it's not the crux of the halting problem. It holds for infinite programs too, because diagonalization arguments don't care how big your set is.
Anyway, I don't really have the energy for this. I appreciate the time and discussion, for which I thank you. But as someone who studied maths at a PhD level and now programs for a living, I'm not getting much out of these ideas. Perhaps we can just agree to disagree for now.