echoone

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Aug 24	comment	what is the geometric idea of this theorem? Isn't this just a generalization of the Mean Value Theorem?
Aug 23	awarded	Yearling
Aug 21	comment	Characterization of Almost-Everywhere convergence Even though you cannot topologize almost everywhere convergence, you can create a convergence space out of it.
Aug 3	comment	odd person out game You have not told us what p is?
Jul 26	comment	The Star Trek Problem in Williams's Book Why not try the problem in the one-dimensional setting and see what happens?
Jul 19	awarded	Critic
Jul 4	comment	History of Dual Spaces and Linear Functionals @MattE I like that explanation. In fact, that is exactly how it was done historically according to the stuff I have read.
Jul 4	comment	Finding the point of impact between two object with constant velocity, where only angle is variable That means there are two variables, the launch-angle of B and its position relative to A. That makes the problem harder. I suggest fixing one of them and solving for the other. Note that the range of A and the range of B must overlap since their paths must at least cross each other.
Jul 4	comment	Finding the point of impact between two object with constant velocity, where only angle is variable Are A and B being launched toward each other? How far are A and B apart?
Jul 4	comment	Dimension of a cyclic submodule of a finite group representation Isn't it true that the span of $\{\rho_g v : g \in G, v \in V\}$ is equal to the span of $\{\rho_g v : g \in G, v \in B\}$ where $B$ is any basis of $V$? If $G$ is finite, then you can compute the dimension of this latter span by checking for linear independence of the vectors in $\{\rho_g v : g \in G, v \in B\}$.
Jul 4	comment	Bound on $E[X Y]$, where $Y$ is bounded in terms of $X$ If $X \ge Y^k$, then $XY \ge Y^{k+1}$ and so $E[XY] \ge E[Y^{k+1}]$. I don't know what to do with $E[Y^{k+1}]$ though.
Jul 3	comment	History of Dual Spaces and Linear Functionals Nice. I will definitely have to read that book.
Jul 3	answered	History of Dual Spaces and Linear Functionals
Jul 2	comment	History of Dual Spaces and Linear Functionals I disagree that the concept of a linear functional occurs "everywhere". The two examples you gave are well and good but they will not force me to start thinking about linear functionals in general. I am wondering what Riesz's motivation was in producing the RRT. You mention that the RRT can be used to define the cross product using determinants. I find that interesting. Do you have a reference?
Jul 2	comment	History of Dual Spaces and Linear Functionals If I were exploring the difference between row vectors and column vectors, I would make two observations: row vector x column vector = scalar and column vector x row vector = matrix. That this would lead me to the concepts of linear functional or dual space seems unlikely to me.
Jul 1	asked	History of Dual Spaces and Linear Functionals
Jun 13	comment	Union of compact sets in a convergence space Ah, of course! Thanks a lot.
Jun 13	accepted	Union of compact sets in a convergence space
Jun 13	comment	Union of compact sets in a convergence space This is true if the convergence spaces are topological by the argument you just gave. The general case though...
Jun 13	asked	Union of compact sets in a convergence space