this post was submitted on 25 Aug 2024
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No, because borders are made up by humans and humans can't write down or even measure infinitely small
Some borders drawn as straight lines on maps sure. But we also define borders by rivers and all sorts of other fractal things.
Borders are just social construct
We can if we make tools to do it for us.
halting problem
Actually, in this case, it's easily solved. Trying to measure an infinitely complex curve will never halt, answer found.
No, I can write limits.
It's kind of subtle how exactly you're using numbers when writing limits. You're either not actually doing infinitesimals, just Cauchy sequences centered around a point, or you are and you get to enjoy the axiomatisation of the hyperreals.