monoidal-monoidoidoid

[monoidal-monoidoidoid]

analysis is really cool on like an aesthetic level but I swear to god if I have to write one more proof of convergence

[monoidal-monoidoidoid]

my Analysis II professor just started drawing commutative diagrams I'm so excited

[monoidal-monoidoidoid]

in abstract algebra, if an "X" is some structure that can be seen as a one object category, then an "X-oid" is often a similar structure, but with an underlying category made up of arbitrarily many objects. for example, a group can be viewed as a category with invertible morphisms and exactly one object, so a groupoid is any category with invertible morphisms, which could in general contain many objects. other common examples are "vocaloids", which are made up of many vocals, and "utauloids", which are made up of a lot of singing.

[monoidal-monoidoidoid]

[monoidal-monoidoidoid]

compresses you

f-fuck...your discrete cosine transform, it's s-so fucking efficient...

[monoidal-monoidoidoid]

its even worse btw u dont even need to define a -cow if you just define 2 cows or whatever prime number to be zero (i.e. if u have 2 or well prime number of cows u can put them away in some kind of amazing grasslands) and u get a vector field. of cow.s

[monoidal-monoidoidoid]

i think maybe we could spend less time thinking about things that make us angry and more time thinking about other stuff

[monoidal-monoidoidoid]

REBLOG THIS POST IF YOU ARE A MATH ENJOYER

No it is not optional, I desperately need to follow y’all so that there is more math on my dashboard.

[monoidal-monoidoidoid]

it feels odd that categories are the only "popular" algebraic structure that explicitly allow the underlying collection of stuff to be a proper class instead of a set - is there a good reason why thats generally accepted only in the case of categories? (I guess besides the fact that a lot of the big important categories just happen to be categories defined on proper classes and so we define the term "category" to explicitly allow those)

do categories somehow lead to fewer problems than proper class "fields" like the surreal numbers do?

[monoidal-monoidoidoid]

oh yeah? well, how does your "set theory" explain this:

[monoidal-monoidoidoid]

This "algorithm" I am reviewing has a worst-case time complexity of O((2^(2^n))^10). I sort of just want to restate that in the weaknesses box for the review of the paper, leave the other boxes blank, and submit that as my review. But I guess that would be antisocial.

[monoidal-monoidoidoid]

#mytome!!!!

[monoidal-monoidoidoid]

#mytome!!!!

[monoidal-monoidoidoid]

whenever a linear algebra professor catches you having too much fun with math they are legally obligated to make you do gram-schmidt as a way of humbling yourself

[monoidal-monoidoidoid]

whenever a linear algebra professor catches you having too much fun with math they are legally obligated to make you do gram-schmidt as a way of humbling yourself

[monoidal-monoidoidoid]

Am I correct in assuming that if you want to rigorously derive formulas for calculating volumes of arbitrary n-dimensional polytopes (or to even formally define what a volume is in the first place) you need to get into measure theory? Or is there a simpler, more algebraic way that still leads to a fully formal and rigorous proof?

(I'm specifically interested in a rigorous proof that the correspondence between determinants of n x n matrices and volumes of n-parallelotopes spanned by the corresponding vectors continues to hold for arbitrary n)

[monoidal-monoidoidoid]

Am I correct in assuming that if you want to rigorously derive formulas for calculating volumes of arbitrary n-dimensional polytopes (or to even formally define what a volume is in the first place) you need to get into measure theory? Or is there a simpler, more algebraic way that still leads to a fully formal and rigorous proof?

(I'm specifically interested in a rigorous proof that the correspondence between determinants of n x n matrices and volumes of n-parallelotopes spanned by the corresponding vectors continues to hold for arbitrary n)