Talk:Height: Difference between revisions
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: Could you provide some materials on what it is? [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 07:49, 31 December 2022 (UTC) | : Could you provide some materials on what it is? [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 07:49, 31 December 2022 (UTC) | ||
== Counterexample == | |||
Not sure how relevant this is, but I was wondering why we have "height" and "complexity" as different things. A counterexample might clear up the difference. Consider the total number of prime factors of a number. This is some kind of complexity measure. It's really just the unweighted l_1 norm when expressed in vector form, so it seems quite sensible. For example 5/4 = 2^-2 * 5^1, so h(5/4) = 3. Similarly we have h(81/80) = 9. This satisfies all of the criteria except finiteness, all prime numbers p have h(p/1) = 1. So there are infinitely many rationals for which h(x) <= C. | |||
So this defines a complexity which is not a height. | |||
– [[User:Sintel|Sintel🎏]] ([[User_talk:Sintel|talk]]) 13:41, 25 April 2025 (UTC) | |||