Since you feel so strongly about it, let me argue that you're simply wrong:
Infinities have the opposite effect then you might think, they make things simpler. It's much easier to reason about an infinite list of numbers then to reason about 64 bit numbers.
In analysis, it's much easier to reason about infinitely differentiable, or smooth, surfaces then very rigid and complicated services.
The fact that infinities cause some complications in the foundations itself is a drop in the bucket to the practical application and simplifications of day to day mathematics.
> Infinities have the opposite effect then you might think, they make things simpler. It's much easier to reason about an infinite list of numbers then to reason about 64 bit numbers.
I would argue that a few extra lines in a proof is a small price to pay to avoid the Godelian catastrophe.
Infinities have the opposite effect then you might think, they make things simpler. It's much easier to reason about an infinite list of numbers then to reason about 64 bit numbers.
In analysis, it's much easier to reason about infinitely differentiable, or smooth, surfaces then very rigid and complicated services.
The fact that infinities cause some complications in the foundations itself is a drop in the bucket to the practical application and simplifications of day to day mathematics.