Stefan

Mathematician building satellites - ex DLR; former electrical engineer; likes to play with programming languages; reads too much

[Stefan @lSV_97]

@FissionableFrog @DiracGhost It allows you to do linear algebra over things that aren't fields. Classic example from differential geometry: smooth (or whatever you want) functions as a ring, differential forms as a module over that ring

[Stefan @lSV_97]

@FreyaHolmer I think this would be considered "(re)normalization" in some systems. Maybe also "realize" or smth given that it's a form of lazy initialization? (Tbh I'd avoid the situation by using a distinct type with conversion function instead if at all possible)

[Stefan @lSV_97]

@alexwebber @yacineMTB @OatmealThief Mostly any book should have some. Linear algebra done right by Axler is free and has exercises after every section.

[Stefan @lSV_97]

@TonyTheLion2500 Note that at least locally any "curve set" is the image of a "curve function" and we can mostly identify the two with one another

[Stefan @lSV_97]

@TonyTheLion2500 Depends on the author but I'm inclined to say yes. Usually curves in diffgeo are (strictly speaking) defined as 1-dimensional (sub-)manifolds - so sets. However very commonly we also refer to their parametrisations (so certain functions whose image is the curve set) as "curves".

[Stefan @lSV_97]

@chacha72kobe4er @LogKa11 "No specialized lens"? You may want to take another look at those glasses: they are still fitted shooting glasses, just a different style.

[Stefan @lSV_97]

@pydomantwo @BuzzTwice71638 @heronyc @LogKa11 It's also for the guns. PCP airguns are loud enough to damage your hearing over time

[Stefan @lSV_97]

@seungylee14 @MikeIsaac It is very small which has the advantage of allowing for higher muzzle velocities without cranking up the energy

[Stefan @lSV_97]

@bending_michael @FreyaHolmer 1-cos(pi/n) which quickly converges to 0. This then implies the uniform convergence of these functions to regular sine and cosine

[Stefan @lSV_97]

@bending_michael @FreyaHolmer Yes - even uniformly (a strong form of convergence for functions). A regular n-gon with circumradius r has an inscribed circle of radius r cos(pi/n). Hence the maximal deviation between circle and n-gon along any line through the origin can be no more than a constant multiple of

[Stefan @lSV_97]

@Valuable @FreyaHolmer And similarly we can justify the "it's exponential" because locally we can express it as an exponential with very good error bounds

[Stefan @lSV_97]

@Valuable @FreyaHolmer It's not that "we can find a best linear approximation" it's about how good of an approximation we actually get. With sigmoids the approximation is generally speaking quite good since higher order components decay very rapidly. The logistic function is linear - x³/48 + O(5)

[Stefan @lSV_97]

@fasterthanlime It may be too niche but ATS can do this AFAIK, it has linear types.

[Stefan @lSV_97]

@just_lollin @crypt0potamus @ItsSharples @theodorebeers @emil_priver A type error

[Stefan @lSV_97]

@crypt0potamus @ItsSharples @theodorebeers @emil_priver If only there was a way to deal with different order structures that didn't involve mutilating your standard sort in a way that it can't sort basic numbers...

[Stefan @lSV_97]

@akivaw @LongFormMath Beta I agree but Ypsilon is a thing. It's called \Upsilon in latex (there's also a var variant)

[Stefan @lSV_97]

@akivaw @LongFormMath Would it be okay to use Υ (capital greek Ypsilon) instead of the latin Y?

[Stefan @lSV_97]

@BruvverEccles @fermatslibrary Just use parantheses for those :)

[Stefan @lSV_97]

@lilchiva @Dandy_Roddick @TonyTheLion2500 It confidentally tried to tell me that 3>4 today as part of and example and corrected itself to 2>3 or smth like that. It's still terrible at the most basic things (it can still be useful though)

[Stefan @lSV_97]

@Algon_33 @davidad @JadeMasterMath @josephjdavies For integration: it kind of makes sense that C on compact sets would be fine imo but I wouldn't be surprised if physicists also wanted to do this stuff on noncompact domains(?)

[Stefan @lSV_97]

@Algon_33 @davidad @JadeMasterMath @josephjdavies For deriatives we'd need the C^infty to be able to iterate them - but I'm not sure if we'd have the boundedness in this case (probably not?). I could see this leading into schwarz spaces or smth - just guessing though, I never really studied functional analysis.