Kogasa
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Yeah, it’s a matter of convention rather than opinion really, but among US academia the convention is to exclude 0 from the naturals. I think in France they include it.
I understand those are food words but I’m incapable of picturing those things in combination as a food item
As long as we can put an upper bound on gayness (or more specifically on each totally ordered subset of people under the is-gayer-than relation) this follows from Zorn’s lemma.
It’s also true by virtue of the fact that the set of all people who will have ever lived is finite, but “the existence of a maximal element in a poset” just screams Zorn’s lemma.
2·2 months agoIt’s a different situation, as a dev I’d happily bet my life on this assumption.
Dropping support for that stuff means breaking 95% of the websites people currently use. It’s a non-starter, it cannot ever happen, even if you think it would be for the best.
Math builds up so much context that it’s hard to avoid the use of shorthand and reused names for things. Every math book and paper will start with definitions. So it’s not really on you for not recognizing it here
🍕(–, B) : C -> Set denotes the contravariant hom functor, normally written Hom(–, B). In this case, C is a category, and B is a fixed object in that category. The – can be replaced by either an object or morphism of C, and that defines a map from C to Set.
For any given object X in C, the hom-set Hom(X, C) is the set of morphisms X -> B in C. For a morphism f : X -> Y in C, the Set morphism Hom(f, B) : Hom(Y, B) -> Hom(X, B) is defined by sending each g : Y -> B to gf : X -> B. This is the mapping C -> Set defined by Hom(–, C), and it’s a (contravariant) functor because it respects composition: if h : X -> Y and f : Y -> Z then fh : X -> Z and Hom(fh, C) = Hom(h, C)Hom(f, C) sends g : Z -> B to gfh : X -> B.
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P^(n)® AKA RP^n is the n-dimensional real projective space.
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The caveat “phi is a morphism” is probably just to clarify that we’re talking about “all morphisms X -> Y [in a given category]” and not simply all functions or something.
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For more context, the derived functor of Hom(–, B) is called the Ext functor, and the exactness of that sequence (if the typo were fixed) is the statement of the universal coefficient theorem (for cohomology): https://en.wikipedia.org/wiki/Universal_coefficient_theorem The solution to this problem is the “Example: mod 2 cohomology of the real projective space” on that page. It’s (Z/2Z)[x] / <x^(n+1)> or 🍔[x]/<x^(n+1)>, i.e. the ring of polynomials of degree n or less with coefficients in 🍔 = Z/2Z, meaning coefficients of 0 or 1.
It’s not nonsense, although there is a typo that makes it technically unsolvable. If you fix the typo, it’s an example calculation in the wikipedia page on the universal coefficient theorem: https://en.m.wikipedia.org/wiki/Universal_coefficient_theorem
Sometimes I update and can no longer boot so I go outside, does that counf
I once had the flu so badly I couldn’t get out of bed or yell for help. My parents put on “Flushed Away” (movie about some fuckin rats) on dvd and it looped at least 4 times before anyone came back to turn it off. One of my core traumas
It’s got a very high barrier to entry. You kinda have to suffer through it for a while before you get it. And then you unlock a totally different kind of suffering.