/sci/ - Science & Math

>>11451432
>I did manage to demonstrate an instance in which Freed-Hopkins's conjecture seems to be true though.
Nice.
>>11451498
>>11451502
>take a moment to check
>the argument doesn't really copy word for word for the general case, even if it kinda resembles it
My bad.
We set [math]Dg(0) = G[/math] (the total differential operator at 0) (technically the linear functional of the inner product with the gradient, but whatever).
For our first estimate, we start with [math]\lim_{||v|| \rightarrow 0} || \frac{g(v) - G(v)}{||v||} || = 0[/math], and we use an absolute bullshit, high illegal trick, known as "passing [math]f(v)[/math] inside because it's continuous to obtain" [math]\lim_{||v|| \rightarrow 0} || \frac{f(v)g(v) - f(v)G(v)}{||v||} || = 0[/math] , which is estimate number one.
Estimate number two is [math]\lim _{||v|| \rightarrow 0} || \frac{f(v)G(v) - f(0)G(v)}{||v||} || = \lim _{||v|| \rightarrow 0} ||\frac{[f(v)-f(0)]G(v)}{||v||} || \leq \lim _{||v|| \rightarrow 0} || \frac{[f(v)-f(0)] ~ ||G|| ~ ||v||}{||v||} || = \lim _{||v|| \rightarrow 0} [f(v)-f(0)]||G|| = 0[/math].
Then you throw in a triangle inequality: [math]\lim _{||v|| \rightarrow 0} || \frac{fg(v) - f(0)G(v)}{||v||} || \leq \lim _{||v|| \rightarrow 0} [ ||\frac{f(v)g(v) - f(v)G(v)}{||v||} || + || \frac{f(v)G(v) - f(0)G(v)}{||v||} ||] = 0[/math].

I think the only weird thing I used is the operator norm. For a reasonable reference, see https://en.wikipedia.org/wiki/Operator_norm
>>11451823
Your professors do that?
A few professors I had literally wrote ~100 pages long books on the subject and had us print them out and use as material for the semester.

>>11384829
It starts from an asspull and finishes with algebra.
Now, an asspull proof can still be good, as long as its sufficiently slick and shorter than properly intuitive proofs.
But literally just substituting x=-b/2a has clear geometry behind it, and is the exact same length.
Thus, the proof is bad.
Note: substituting x=-b/2a isn't good either. It's half decent at best.