The other way to have written the initial proof is to have done the contrapositive: Suppose $s\mathbf{x}+t\mathbf{y}=0$ for $s,t$ not both zero. If $t\neq 0$, then $\mathbf{y}=(-s/t)\mathbf{x}$ and $-s/t\in \mathbb{R}$ so the vectors are parallel. The analogous argument holds for $s\neq 0$ and so the vectors must be parallel.
i have actually seen people who have no idea how to do a question just write every kind of relevant piece of information they could think of in hopes that whilst marking it i will recognize the correct solution.
My old physics prof would give you 9/10 points on a question for writing everything down, and only 1 point for solving/getting the correct answer. It was wierd
@CookieToast I actually agree with the spirit of that, tbh. When grading quiz problems (at least at the intro level) I care more about the setup than the final result.
However, the set-up is more than just "what numbers are given in the problem"
That won't get you very far in my book. But, for instance, properly writing out the kinematic equations in a projectile motion problem is more important to me than if you solve them correctly in a quiz setting. The latter is math, not physics.
@Semiclassical yeah I have no issue with her. And she intentionally structured her exams so we didn't have enough time. I liked that because it really taught me how to work under pressure
It was pretty cool actually. She gave 7 or 8 problems of increasing difficult, but only expected the class to get through the first 4 or 5. But if you were lucky enough to see the trick to one of the more difficult ones, you could set it up for a few extra points.
@Faust You probably aren't going to find a function that is uniformly convergent, but you might find a function that is the uniform limit of a sequence of functions...
So we have this family of maps $i_C : Mor(C,A) \rightarrow Mor(C,A^{\prime})$ where each of the family comes equipped with $f_C$ and $g_C$ that make the diagram commutes
I spent most of my day today making sure that I could prove that singleton sets in $\mathbb{Q}_p$ are fractal in the sense that advisor defines the term
> The New York Times obituary stated that "he added the middle initial himself, though it does not stand for a middle name".[1] But other sources suggest that he intended his middle initial B. to recursively mean Benoit B. Mandelbrot, thereby including a fractal (his mathematical discovery) in his own name.[2][3]
I probably would have enjoyed it if I had more time to actually think about it, but it started getting deep into the weeds of sheaves and stalks and germs way too fast for me
> In 1982, Mandelbrot expanded and updated his ideas in The Fractal Geometry of Nature.[20] This influential work brought fractals into the mainstream of professional and popular mathematics, as well as silencing critics, who had dismissed fractals as "program artifacts".
Mathematicians might want to put more focus on topology constructs, cause these system's lack of dependence on details like geometry might give more insight on how amorphous matter behaves
Imagine an amorphous solid which has an inherent ordering and topology, some kind of collective behaviour might be interesting will take place there
