It is often claimed that 2 is special because it is the only even prime. This is circular because "even" is defined in reference to 2. But the reasons that mod 2 is more interesting than mod n for n≠2 are reasons that 2 is special.
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Replying to @ModelOfTheory
And what are those reasons? The main one I can think of is that the complex primitive n-th root of unity is an integer for n = 2, but not for higher n (and whatever consequences this has). Are there others?
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Replying to @RadishHarmers
Most I can think of are consequences of that, and the related fact that inversion has order 2 (as does "not" in classical logic). Also, parity of permutations is well-defined, but permutations mod n isn't, complex manifolds have no odd-dimensional homology.
4 replies 0 retweets 1 like
"Complex manifolds have no odd-dimensional homology" is false. There may have been a true related fact that I meant to say, but I don't remember.
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