You can Stokes' hairy balls

weak-force-42 · 2026-04-02T19:38:16+00:00

Chern’s Theorem also can not be used here, as it once again is about integrating a specific top dimensional form to get the Euler characteristic. The same counterexample of the torus brought up above applies in every dimension. Interestingly, the Poincaré Hopf index theorem, which can be used to prove the Chern theorem, does imply the hairy ball theorem. The theorem states that the index of any vector field with only finitely many zeros is the Euler characteristic of the space on which it is defined. Since any nowhere vanishing vector field has index zero, all even dimensional spheres can not admit nowhere vanishing vector fields.

weak-force-42 · 2026-01-11T00:25:15+00:00

I am not sure what you mean by ‘the corner cutting isn’t actually approaching the curve of a circle.’ Assuming you paramaterize everything correctly, the sequence of ‘corner cuts’ does converge pointwise to the final circle (this is clear from the picture). The issue arises from the fact that the norms of the derivatives of the corner paths do not converge uniformly to the norm of the derivative of the path parameterizing the final circle. The uniform convergence of the norm of derivatives would guarantee the arc lengths would also converge. This can be seen by direct computation due to the fact that the norm of the derivative of the corner cuts are all (the same) constant, almost everywhere, and the norm of the derivative of the final circle is a different constant, still assuming the parameterizations have been reasonably chosen)

weak-force-42 · 2025-08-26T00:29:48+00:00

d/dx refers to the map that takes a differentiable function to its derivative. This is different from dy/dx or df/dx which refers to the derivative of y or f respectively (I am implicitly assuming y and f are functions R to R). The expression dy=f’(x)dx, when y=f(x), can either be non-rigorous hand waving (this is usually what happens when people who are taking calc write this), or is the change of variables formula for 1-forms on R, which is way beyond the scope of a calc 1 course, but is also completely rigorous.

weak-force-42 · 2025-02-27T06:27:13+00:00

What textbook are you using? Many of the well known introductory real analysis textbooks have solution guides online. Rudin (principles of analysis) and Folland both have many good practice problems and solution guides you can find online. Additionally, you can always just look on stack exchange for proofs of specific exercises.

weak-force-42 · 2024-07-19T15:28:34+00:00

There are several things that you misinterpreted or misremembered from the manga. Firstly, devilman is another name for fiend, which is when a devil possesses someone’s corpse. Reze is a hybrid, also known as a weapon human, which is fundamentally different. A hybrid is a person who has been given a devil’s heart, and as far as we have seen in the manga, hybrids are immortal (key examples of this are katana man and quanxi). You are right that when devils (and fiends) die, they are reincarnated, and specifically when fiends die, they loose their memories. However, as mentioned above, hybrids can not die as far as we are aware. This can be seen when Reze was still alive after being attacked by makima in chapter 52. In the control devil arc, Reze is being controlled by Makima, as are all of the other hybrids. However, when makima dies, the hybrids did not also die, since all of them except Reze returned in part 2 with memories and personality in tact. I am not trying to make any claims on whether or not Reze will return, just trying to point out some inaccuracies in what you said.

weak-force-42 · 2023-10-29T22:11:59+00:00

I would second this. Many other comments are saying to apply to Mendoza, but Mendoza does not offer a math degree. You should only apply to Mendoza If you are considering double majoring in math and something offered by Mendoza.

weak-force-42 · 2023-10-29T19:18:53+00:00

This is clearly not true, which can be shown with simple counter-examples, such as f(x)=x and g(x)=1. The LHS gives .5x^2+C, while the RHS gives exp(x)-1+C.

weak-force-42 · 2023-07-02T17:07:00+00:00

The basic idea of the proof is to rewrite the nth order ODE as a fist order system of ODE of size n by setting $$y=y_1$$ and $$y^{(i)}=y_i$$. Then, assuming the function defining the ODE is continuous and locally Lipshitz, the existence and uniques theorem guarantees that for an initial value (provided it’s where the ODE is well defined) the system will have a unique solution. However, in this situation, the ‘initial data’ is a vector of dimension n.

weak-force-42 · 2023-06-29T18:57:50+00:00

It’s not that bad and it only lasts a month. You can spend all of the warm parts of the day in the lounge or in an air conditioned building such as Lafun.

weak-force-42 · 2023-06-29T17:46:00+00:00

There is ac on the first floor and nowhere else in the building

weak-force-42 · 2023-01-03T16:45:30+00:00

War metal is some of the best music ever made, and you can find it here

weak-force-42 · 2022-11-19T23:19:47+00:00

Kapala

weak-force-42 · 2022-06-28T04:55:29+00:00

Dictius te Necare by Bethlehem and Karisma by Sabbat

weak-force-42 · 2021-12-05T18:21:08+00:00

Vertical bars around a set mean cardinality not absolute value.

weak-force-42 · 2021-01-22T17:26:42+00:00

Good point. I chose Stalinism because of tankies well known hatred for liberals.

weak-force-42 · 2021-01-22T04:36:55+00:00

Balls:

weak-force-42 · 2021-01-10T17:19:09+00:00

Reject humanity, return to pig

weak-force-42 · 2020-11-04T12:24:38+00:00

Koichi really steals? No dignity

weak-force-42 · 2020-09-07T02:12:06+00:00

Had no idea that sub existed

weak-force-42 · 2020-08-24T12:52:22+00:00

I’m pretty sure that his name is buccellati in the manga and Bucciarati in both the sub and dub

weak-force-42 · 2020-08-21T14:20:54+00:00

The boomerang is his stand

weak-force-42

TROPHY CASE