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God created the real numbers

(www.ethanheilman.com)
136 points Bogdanp | 2 comments | 29 Aug 25 15:31 UTC | HN request time: 0.001s | source
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zarzavat ◴[29 Aug 25 19:39 UTC] No.45068473[source]▶
God created the rational numbers.

The universe requires infinite divisibility, i.e. a dense set. It doesn't require infinite precision, i.e. a complete set. Our equations for the universe require a complete set, but that would be confusing the map with the territory. There is no physical evidence for uncountable infinities, those are purely in the imagination of man.

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1. baxtr ◴[30 Aug 25 22:05 UTC] No.45078392[source]▶
A circle seems quite ordinary at first glance, yet its area is pretty irrational.
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2. zarzavat ◴[31 Aug 25 03:58 UTC] No.45080257[source]▶
The area of a circle is a computable number so it can be put into one-to-one correspondence with the rationals. It's much more like a rational number than a real number, insofar as it doesn't require infinities to represent it.

The set of real numbers is almost all extraneous junk that the universe definitely doesn't care about but is very important to mathematicians.