Topology

>topology
can you PLEASE explain to me why this masturbation math exists?

Other urls found in this thread:

youtube.com/watch?v=AmgkSdhK4K8
youtube.com/watch?v=sKqt6e7EcCs
arxiv.org/abs/math/0512103
youtube.com/watch?v=gZpsVSVRsZk
twitter.com/SFWRedditGifs

To give your stupid-ass [math]\lim_{x \,\rightarrow\, a} f \left( x \right)[/math] a meaning.

What a fucking fag. Abstract topology is useful in robotics.

the definition of a limit never needed homoemorphic dick sucking

pfft, clearly no math past ODEs and vector calculus has any application to anything. if it did i would have had to take it for engineering.

Why would anyone need to explain this to you?

Grab a book, read about it. Watch a video about it or read about it in a encyclopedia.

yes this is a bait thread.

But it is imperative that we not thing about topology as being the study of the continuous deformation of geometric objects, but rather as just a souped up set theory which was originally devised to help cement concepts in the theory of calculus.

Calculus is important, hence understanding it and its limitations are important, hence understanding the theory of calculus is important, hence topology is important.

Pretty sure PDEs and differential geometry are used in engineering.
It's not that exotic mathematics is not useful.
From exotic math eventually comes out something useful but that's not work for engineers.

Here's a video that shows how topology can be applied to make a pretty cool solution to a problem.

youtube.com/watch?v=AmgkSdhK4K8

to generalize analysis

lol kill yourself, brainlet.

it's a shame that there are people who unironically believe this

Is the human a klein bottle ? Your anus connects your outside to the inside without crossing an edge.
Thoughts on my theory please.

depends how deep the rabbit hole goes.
i'm satisfied saying that humans are macroscopically a donut with 8 holes.

Idk bro, most of those clealy aren't even real Pokemon

it doesn't actually

you are more of a torus

A 3-torus because of your nasal holes

>klein bottle
No. It can only be embedded in R^4 and higher, otherwise you get self-intersection.

Take your shitty forced meme back to

i have question for topologists

So you take a disc and cut a hole through it. It has one hole.
You take a disc and cut two separate holes in it. It has two holes.
You take a disc and cut a hole through it, then from a different spot on the surface, cut another hole which meets the first hole somewhere, and ends.
It has more holes than 1, and fewer holes than 2. How many holes does it have?

youtube.com/watch?v=sKqt6e7EcCs

this is why topology exists

A 3-torus can't be embedded in R^3 either, kid

I think he meant that the boundary of our body is a surface of genus three. Maybe.

And, OP, topology has applications in physics, logic, computing, data science, optimization, geometry, analysis, and abstract algebra (which further admits application to combinatorics, computer science, and chemistry, to name a few).

Gravity is the riemannian curvature of a lorentzian manifold.

Electromagnetism is the curvature of a U(1) Torsor over spacetime.

Quantum field theories are functors from the category of smooth cobordisms to the category of vector spaces.

etc.

Holy shit what's that 3rd thing

arxiv.org/abs/math/0512103

The weirdly cut hole is still homeomorphic to a single hole.

Did you already consider the navel ?
Would a open navel change the topology of the human body ?

When you're in the womb I suppose. Otherwise the navel is closed (hopefully)

this is just an anime but

youtube.com/watch?v=gZpsVSVRsZk

wow.. now THIS is a good example of topology

maximum kek

I'm in chem eng., and I would've liked to take a course in pde's or differential geometry.

What would you use something as advanced as differential geometry for?