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I give back what I recieve just as the law requires
(lemmy.dbzer0.com)
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this post was submitted on 12 Aug 2023
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Do we have ways of computing orders of infinity higher than ℵ₀?
Crap. Markdown isn't markdowning. Fixed with unicode.
Symbolically, sure, but then you're not dealing with infinities you're just representing them.
It's a meme it's playing fast and loose with things but the general gist is that mathematics, to this day, doesn't really care about Gödel/Church/Turing, incompleteness, the halting problem, whatever angle you want to look at it from. Formalists lost the war and they simply went on doing maths as if nothing had happened, as if a system could be simultaneously complete and consistent. There's people out there preaching to the unenlightened masses but it's an uphill battle.
We have sorta the same problem with imaginary numbers, and I remember some programmable calculators can process complex numbers using symbolic representation (which happens to work similarly to Cartesian coordinates, so that's convenient)
But from what I remember any infinity bigger than counting numbers (say the set of real numbers) cannot be differentiated from each other, so we don't have established rules.
To be fair, I last tinkered with infinities in the aughts and then as a hobbyist. The Grand Hilbert Hotel can accomodate more compound infinities and still retain perfect utilization since the last time I visited.
it's more than convenient, it's isomorphism!