Simple probability question that I believe to have the correct solution to... Given a string of 12 light bulbs, with 3 of the 12 randomly burned out, what are the odds that the 6th bulb in the string is the 3rd and final faulty bulb?
But immediately before he was talking about everything being done in char 0, is it that even over a generic char 0 field you can somehow transfer things to $\mathbb{C}$ or is it just that he was thinking about $\mathbb{C}$ but aside from part 2 of Schur, he'd be alright with whatever
As I discuss in the book, conjugating is like changing coordinates ... like the change of basis formula in linear algebra. But just do it. Conjugate a rotation by a reflection and draw it out.
@Daminark $kG$-modules $V$ are the same as representations $G \to \text{GL}(V)$ for some $k$-vector space $V$ regardless of the characteristic of $k$, innit
Maybe, but when you trivialize the tangent bundle, it would be nice to use parallel vector fields or 1-forms so that we know the latter have 0 derivative. If you just take a random trivialization, you're not going to have any bracket control.
In this paper1 on the history of functional analysis, the author mentions the following example of an infinite system of linear equations in an infinite number of variables $c_i = A_{ij} x_j$:
\begin{align*}
\begin{array}{ccccccccc}
1 & = & x_1 & + & x_2 & + & x_3 & + & \dots \\
1 & = & & &...
This interesting question is still not getting any answers, and it is countably many dimensions. I guess for uncountably many, it will be even trickier
I wonder where are the functional analysis people in this chat went
they will probably need to wander for a long time before finding their way back here
Meanwhile, Leaky, simpleart and I were somewhere in the wilderness, near some amorphous sets. We also brought some ordinals as rulers for a safe measure
Basically, turns out that in a meaningful sense, partially ordered sets, Alexandroff T_0 spaces, small categories, and ordered simplicial complexes are the same thing