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 Jul4 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 $\{\rho_g v : g \in G, v \in B\}$. Jul4 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. Jul3 comment History of Dual Spaces and Linear Functionals Nice. I will definitely have to read that book. Jul3 answered History of Dual Spaces and Linear Functionals Jul2 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? Jul2 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. Jul1 asked History of Dual Spaces and Linear Functionals Jun13 comment Union of compact sets in a convergence space Ah, of course! Thanks a lot. Jun13 accepted Union of compact sets in a convergence space Jun13 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... Jun13 asked Union of compact sets in a convergence space Jun8 awarded Caucus Jun1 comment Continuous and Open maps A continuous function that maps open sets to open sets is just called an open map as far as I know. Apr20 comment Is there a way of defining the notion of a variable mathematically? Thanks for the example. However, I am not convinced this clarifies what a variable is. Calling the symbol $x$ a variable when defining a polynomial ring $F[x]$ does not define what a variable is. Apr20 accepted Is there a way of defining the notion of a variable mathematically? Apr19 comment The topology of distributions Excellent. Thanks. Apr19 comment Is there a way of defining the notion of a variable mathematically? I do not see the connection. Can you give me a concrete example? Apr19 comment Is there a way of defining the notion of a variable mathematically? I think I understand what you are getting at. If we take an informal expression with variables and make it formal ala metamath, we would get some string of symbols involving those variables, which is just a string in some formal language. Thus, in the language of metamath, a variable is any greek and roman letter that appears in a string of that language. Apr18 asked Is there a way of defining the notion of a variable mathematically? Apr18 revised The topology of distributions deleted 59 characters in body