I have just discovered (during homeschooling) that my children are being taught at school that infinitely many numbers exist. Where do I have to send my petitions against this devastating creationist pre-Hilbertian falsehood?
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Replying to @satvikpendem
For a thing to exist, it is insufficient to specify it, it also needs to be implemented. Infinities can only be specified, not implemented.
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Replying to @sp_deactivated
Your mind can only store finite amounts of information, so ideas that need infinite amounts of information to be represented cannot exist in it.
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Replying to @Plinz
What you've got to realize is that infinities are the end result (or limit) of a process. If the universe is a Zeno machine (if it turns out that in the limit computation is in fact unbounded), then infinities could in fact be implemented at the limit. https://en.wikipedia.org/wiki/Zeno_machine …
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Replying to @zarzuelazen @Plinz
So , I think mathematicians are simply exploring the space of all possible worlds. Given that there's at least one possible world (where the universe is a Zeno machine) in which infinities could actually be implemented physically, that's enough to clinch their existence.
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I don't think that a world that cannot be constructed in any kind of language can exist in any way that would be observable.
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