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God created the real numbers

(www.ethanheilman.com)
31 points EthanHeilman | 1 comments | 28 Aug 25 14:57 UTC | HN request time: 0s | source
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tshaddox ◴[28 Aug 25 18:05 UTC] 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 ◴[28 Aug 25 18:55 UTC] 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. tshaddox ◴[28 Aug 25 19:39 UTC] No.45056188[source]▶
I'm not suggesting the two formalisms should be equally simple. But surely it's not controversial to claim that formalizing the reals involves much more advanced mathematics (and runs into much deeper problems) than formalizing the integers. I'd argue that this disparity is slightly surprising, given that both the integers and the reals are ubiquitous in essentially all branches and levels of mathematics.