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

I do things.


Dec
18
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).
Dec
18
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?
Dec
18
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 $K.$
Dec
18
answered Find a simple expression for the exponential generating function $\bar{C}(x)=\sum_{n\geq0}c_n\dfrac{x^n}{n!}$.
Oct
17
awarded  Yearling
Aug
29
comment Triangle inequality question on norm space
It's incorrect - the first step should be computed as $\parallel \alpha v \parallel = (\alpha x)^2 + (\alpha y)^2.$
Aug
29
comment Triangle inequality question on norm space
You might want to double check N3)
Aug
27
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 $?
Aug
27
revised Finding minima and maxima of $\sin^2x \cos^2x$
edited body
Aug
27
comment Finding minima and maxima of $\sin^2x \cos^2x$
Understandable - I just found this to be a little less messy.
Aug
27
answered Finding minima and maxima of $\sin^2x \cos^2x$
Aug
24
answered Algebraic Topology: CW complexes and their associated $n$-skeletons questions.
Aug
6
comment prove the product $\sin^2\frac{(k-j)\pi}n$
Using the imperative mood might not endear you to potential answerers.
Jul
24
comment Supremum of a sequence
Now surely you don't mean all of that
Jul
24
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 $f.$
Jul
7
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.
Jul
7
comment How to find the $x^2+y^2=?$
I don't understand what you mean.
Jul
6
awarded  Nice Answer
Jul
6
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.
Jul
6
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?