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God created the real numbers

(www.ethanheilman.com)
31 points EthanHeilman | 1 comments | | HN request time: 0s | source
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tshaddox ◴[] No.45055139[source]
Isn't this article conflating our formalism of a given abstract entity (like real numbers or integers) with the abstract entity itself? Surely quantities existed long before humans (e.g. there was a quantity of stars in the Milky Way 1 million years ago). And surely ordinals existed long before humans (e.g. there was a most massive star in the Milky Way 1 million years ago).

The article's claim seems to be about the mathematical formalisms humans have invented for integers and real numbers. And I agree that our formalism of integers is simpler and more elegant than our formalism of real numbers. But that could just be because we've done a worse job formalizing real numbers!

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john-h-k ◴[] No.45055680[source]
> And I agree that our formalism of integers is simpler and more elegant than our formalism of real numbers. But that could just be because we've done a worse job formalizing real numbers!

Everything you can express in integers you can express in reals, but there are many things expressable in reals not possible in integers. It would be surprising if the formalism for a thing that completely supersets another thing had an equally simple formalism

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1. orlp ◴[] No.45056150[source]
Actually in math it's very common for the more general system to be simpler. Compare for example the prime numbers with the integers, or general groups with finite simple groups and the monster group.