Mathematics doesn't actually make any sense

This was great fun! .... I'm so glad I got into Physics!

It's a Ghostblood

this was a great video to pretend i understood while watching

There was a lot that I didn't follow but thanks for the humour.

I'm dying from laughter, thanks for making these! LMAO

What a brilliant video! This got me thinking, why not define a set object as any object X that is isomorphic to the exp object [1, X]. Then we could define a coset as being any object isomorphic to the coexp object: Y ≈ ]Y, 0[

I must admit, this one went over my head

Entropy !

okay i am barely wrapping my head around differential calculus and trying to relearn it after forgetting it 5+ years after learning it.
Isnt this just sign flipping? Why is there even a need for a term for this? I am COnfounded

Isn’t it obvious? The opposition of a set is a knot.

topos with a monoid subobject classifier of cardinality greater than three

There is nothing more irritating than blending pictures in just for a few frames

Some great memeification in this one! 👍

You need some fine nections to pull this off! 👏

jPerhaps you could make a video relating this material to locale theory, perhaps with hints of how that leads to topos theory. My vague understanding is that a locale works on complete Heyting algebras (a frame), but the morphisms can't keep track of both top and bottom at the same time, So a geometric morphism forgets bottom, or something. I think a Heyting algebra is something like an unquotiented preset, while a Boolean algebra quotients by the equivalence relation of symmetric edges to get an antitisymmetric poset. This models extensionality, whereas Heyting algebras allow modeling intensional phenomena, like language.

Co-Conciousness, anybody? 🤔

Nice! I didn't know about this.

Subscribed!

if a comet is a cool space rock that looks pretty should we call all non space boring rocks mets?

u wot m8

I'm too co-co to understand this.

i counderstood this

Why is category theory so much more opaque than every other field of math?? Even the wikipedia articles seem like they're trying NOT to be understood

So, lets assume I manage to understand this information and transform it into knowledge. Could you suggest an example how it could be used to optimize code/program structure for example?

its a rep

Great content but WAAAY to much black screen and 1-second-flashing core content.

Stop the flashing, show us what you're talking about so the brain can process it.

YT it's no radio, we want the visuals in addition to the narration.

Hey G. Could you do a video outlining what topics someone should study if they want to understand more in depth some of these videos.

Would be nice if there were some more beginner friendly videos as well.

I initially thought this is about "Anti-Set Theory", which I read about on the "Rising Entropy" blog.
I recommend it.

"as the name implies" LMAO
I wish I could go back in time to my intro abstract algebra course so I could use this joke.

This reminds a lot of when I was doing topology and measure theory. We define measurable and continuous via the preimage of the function. A lot of the properties we proved seemed less like properties of the actual subject, and more like properties of taking the preimage.

I distinctly remember rediscovering how taking the preimage of an intersection/union is the same as taking the intersection/union of preimages. My first thought was: "damn, the preimage defines a cool function from Y to P(X)". I never thought to think of it as defining a special kind of function from P(Y) to P(X), which I now discover is just the reversed arrow of the original function in the opposite category of "cosets".

cozero

That was the most entertaining math video I watched in a long time. The memes are perfect!

The opposite of a set is worth one penny.
Because it's a sen't.

singleton design (anti)pattern reference during a spiel about caba is so insanely fucking niche hahahahah - and yet im here for it

Honestly, I think the cotangent bundle isn't actually as bad as the tangent bundle. The construction of the tangent space at p is much more messy, and half the time they don't tell you that it's just a set of directional derivative operators at p in local coordinates. The cotangent space at p is just linear maps (cotangent covectors) that identify components of tangent vectors.

To me personally, the opposite of a set has always been a pro-finite set.

Ok, I majored in physics, and 99% of the time I dont have any idea what you are talking about. On the other hand, it really sounds interesting, and the way you cover a subject is very entertaining

The coset is an opp fr

Okay - I return with Conditional Universal Set exists and is compliment of union of all conditional null sets.
And meekly offer: your videos are like fine wine - they do not spoil with ageing and returning to them is as enjoyable as discovering them in first instance.
I think this one might be motivating?
Set of Surreal Numbers and Coset of Surreal numbers?
And surreal numbers in reverse. In sense of day 1 starts with nothing and day infinity starts with many is usual flow in creating surreal numbers.
So change the flow: on day 1 start with many and day infinity ends with one
ps: I hope I never implied I could count 🙂

Looking forward to the sequel: "What's the opposite of a category?" (I presume that the 2-functor sending a category to the category of Functors into the commutative triangle diagram category produces a 2-equivalence of Cat^op to some kind of 2-boolean algebra, but I'd like to hear the details)

Most of this video is good but I think the beginning misses a key part of exploring new mathematical ideas: what part of the structure are you interested in? If you are interested in sets as collections of labels with no other structure, Set^op is a good candidate as that's all arbitrary functions between sets preserve. But when starting out you should always pause to ask whether Set (or whatever concept you're dualising) is the thing you actually care about. Maybe there's more to sets than arbitrary functions between them. For example, if I was studying models of set theory, I might care about the natural internal graph structure of sets: draw an edge from x to y if x∈y. If you make that transitive and reflexive, now every set is naturally a small category and the functions between them are functors, i.e. functions f : X -> Y so that if x ∈ y in X, then f(x) ∈ f(y) in Y. Now there are 2 layers where dualising can happen: at the global level by dualising the entire category of sets, or at the local level by dualising the internal structure of sets. The axioms of set theory give you more places to dualise. Foundation says the internal graph structure is well-founded, i.e. every non-empty subset (subcategory) has an ∈-minimal element. Equivalently (given choice), there's no infinite descending chain x_0 contains x_1 contains x_2 ... If you dualise that, you get a new combinatorial object. Even a brief mention that there are other ways to dualise would've been nice. Another place where you can dualise at two levels and not get the same result is algebras. Sure, the coalgebra is a dual concept to an F-algebra, but in general it's not true that F-Alg^op (dualising the global structure given by algebra homomorphisms) is equivalent to F-Coalg (dualising the local structure). To a newcomer, it might seem initially obvious that those categories are equivalent because the local structures are dual. Adding something like that would improve the video

Your inclusion of the great Bishop Bullwinka when I did in fact assume the law of the excluded middle ended me. I’m still crying.😂

Wait coprime was supposed to mean something different!