question for you guys: Of the games you've played, which has had the best modding priority system?
Like, in Skyrim, its absolutely terrible: its based off of the order the player puts the mods
In Factorio, it's definitely better: you can define your dependencies, dependencies are ordered, and then 3 files are called: data.lua, then data-updates.lua, then data-final-fixes.lua. That said, the purpose of the last two files is to update data from mods that you didn't define a dependency on, which means that its basically a priority system, so everybody puts their stuff in data-final-fixes, which makes data-updates basically useless
To be more mathematically rigorous, once we find the cutoff such that f(n) < n, this doesn't entirely give the cutoff value for the sequence, since there might be an m<n such that f(m) = n. Meaning that there's still ways for a cycle to include numbers above the cutoff if they manage to jump up there... but you would have already found those cycles by searching the numbers below the cutoff.
The main point is that no cycle exists which only uses numbers above the cutoff.
@trichoplax Composite means that you have more than one prime factor (including multiplicities), you could already say that 2^n are all composite for n>1. But this was actually not really a serious proof, it was just about the punchline "don't add one":)
I actually do not have the impression that people from "top" universities are any better in their subject than others (well I can only speak for math) but it is rather the financial means an linked with that the reputation that distinguishes the universities.