opfez on Nostr: ah, yeah shorting fractions isn't necessary, it's just that by their definition, a ...

ah, yeah shorting fractions isn't necessary, it's just that by their definition, a fraction (np)/(nq) = (mp)/(mq) for any n, m. this allows shortening, but doesn't require it, like you note. if you're ever curious, i'd recommend taking a look at the constructions of our numbers (ℕ, ℤ, ℚ, and most importantly ℝ) at some point! you already know ℕ from the peano axioms but it gives a lot of deep insight into a lot of mathematics rather quickly :)