# Tim Duff

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bio website math.stackexchange.com/users/… location Sarasota, FL age 22 member for 2 years, 6 months seen Apr 10 at 8:36 profile views 349

I do things.

# 295 Actions

 Dec18 comment Property of integral and integrator. (NET June 2011) The theorem should be discussed in any text on measure theory. You'll probably see uniform boundedness replaced with pointwise boundedness by a non-negatative integrable function - I don't know of a cleaner proof for the special case in 4). Dec18 comment Property of integral and integrator. (NET June 2011) If we're talking about the Lebesgue integral, $\displaystyle\int_0^1 f$ exists for the first example since it constant almost everywhere. Have you studied the dominated convergence theorem? Dec18 comment Proving a polynomial is algebraic over a tower of fields I think you might be confused about the definition of an algebraic extension. $F/K$ is algebraic if ~every~ element of $F$ is algebraic over $K.$ Dec18 answered Find a simple expression for the exponential generating function $\bar{C}(x)=\sum_{n\geq0}c_n\dfrac{x^n}{n!}$. Oct17 awarded Yearling Aug29 comment Triangle inequality question on norm space It's incorrect - the first step should be computed as $\parallel \alpha v \parallel = (\alpha x)^2 + (\alpha y)^2.$ Aug29 comment Triangle inequality question on norm space You might want to double check N3) Aug27 comment Quadratic forms of two matrices are equal then the matrices are equal The quadratic forms are functions, so they're equal iff they have the same value at each point of $C^n.$ What values do you get for $x = (x_1, \ldots , x_n)$ with $x_i = x_j = 1$ and $x_l = 0$ for all $l\ne i,j$? Aug27 revised Finding minima and maxima of $\sin^2x \cos^2x$ edited body Aug27 comment Finding minima and maxima of $\sin^2x \cos^2x$ Understandable - I just found this to be a little less messy. Aug27 answered Finding minima and maxima of $\sin^2x \cos^2x$ Aug24 answered Algebraic Topology: CW complexes and their associated $n$-skeletons questions. Aug6 comment prove the product $\sin^2\frac{(k-j)\pi}n$ Using the imperative mood might not endear you to potential answerers. Jul24 comment Supremum of a sequence Now surely you don't mean all of that Jul24 comment Lefschetz number What definition are you using for Lefchetz number? I only know of it as the trace of the induced map on homology groups with rational coefficients. In this case you can see that this definition coincides with the Brouwer degree of $f.$ Jul7 comment Motivation for linear topological spaces. In consideration of the Noetherian condition, filtrations show up all of the time in module theory. The important realization is that these filtrations give a linear topology in which it makes sense to define Cauchy sequences (and thus completions) algebraically. Thus some topological intuition can be utilized in passing to the completion of a ring, which isn't manifest in the inverse limit definition. Jul7 comment How to find the $x^2+y^2=?$ I don't understand what you mean. Jul6 awarded Nice Answer Jul6 comment What could be a monotonic, continuous and smooth function with these conditions? It isn't clear whether or not $m$ is fixed or even an integer. Jul6 comment How find $a_{n}$ if $a_{n+1}=\sqrt{2a_n+1}$ This question ought to be rephrased in order to receive a satisfactory answer. You've given a completely satisfactory definition of $a_n$ as the general term of a well-defined sequence. Are you looking specifically for a non-recursive expression?