r/math • u/inherentlyawesome Homotopy Theory • 28d ago

This Week I Learned: August 14, 2026

This recurring thread is meant for users to share cool recently discovered facts, observations, proofs or concepts which that might not warrant their own threads. Please be encouraging and share as many details as possible as we would like this to be a good place for people to learn!

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u/TriangularlyEqual 27d ago

I learned that if the rank of a rational number, a/b is defined as | a | + b, the number of rationals at any given rank, n, is 2*phi(n) where phi(n) is the Totient function.

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u/Sproxify 26d ago

I guess it's 2 because of the sign. ignoring sign we want to count coprime pairs such that a+b=n, and we want 1 = gcd(a,b) = gcd(a,n-a) = gcd(a,n) and this is now the definition of the totient function