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I fill in "About Me" sections from time to time.


Aug
17
answered $ab\equiv 1\pmod{m} \implies a^q\not\equiv 0\pmod{m}$?
Aug
9
comment How prove this integral $\int_{0}^{1}\frac{x^m\ln{x}}{x-1}dx=\sum_{r=m+1}^{\infty}\frac{1}{r^2}$
You can exchange the order of integration if you consider the series expansion for $\log(x)/(1-x) = \sum \log(x) x^n$ converges uniformly for $|x|<1-\epsilon$ and that the leftover part of the integral must be small since $\log(x)~(1-x)$ for $x$ near $1$.
Aug
9
comment How should I continue on with this proof by contraposition?
Yes! You swap the $p$s and $q$s. As mentioned elsewhere, you were trying to show the converse, which is "not p implies not q" (and which is equivalent to "q implies p" using the contrapositive).
Aug
9
comment How should I continue on with this proof by contraposition?
There is absolutely no reason this should be voted to be closed. This is an excellent question and the person asking the question has shown plenty of work.
Aug
9
answered How should I continue on with this proof by contraposition?
Aug
2
comment Calculate $\int \log(1+\log(x))x^ndx$
Well, for $|\log(x)| < 1$ you can use the Taylor series of $\log(1+x)$.
Jul
29
comment How prove such $f(x)g(x)$ coefficient is $1$ or $-1$
Are zero coefficients allowed as well? Because if you look at the constant terms of the polynomials, you must have them be $\pm 1$ which is not more than 2014.
Jul
28
accepted Feynman's Algorithm for computing a logarithm of a number in [1,2]
Jul
28
comment How to compute 1/7 in base 8?
1=0.77777777...? That's crazy. Next you'll be telling me 1=0.99999999...
Jul
28
revised Feynman's Algorithm for computing a logarithm of a number in [1,2]
edited title
Jul
27
comment Feynman's Algorithm for computing a logarithm of a number in [1,2]
Great! If no one comes up with a way to interpret the factors as unique in a couple days, or you don't update this, then I'll accept this answer. Perhaps if you require a finite number for factors, but allow factors to be repeated, then you'll get uniqueness.
Jul
27
comment Feynman's Algorithm for computing a logarithm of a number in [1,2]
@semiclassical A finite number of digits is not a requirement. At any rate, whatever makes it work, if possible, is what is meant.
Jul
27
comment Feynman's Algorithm for computing a logarithm of a number in [1,2]
@littleO, see the link to the essay for all the context I know. It was related to a startup company trying to do parallel computing. In that case it'd be convenient to compute $\log(1+a_k 2^{-k})$ and then multiply together.
Jul
27
revised Feynman's Algorithm for computing a logarithm of a number in [1,2]
added 4 characters in body
Jul
27
asked Feynman's Algorithm for computing a logarithm of a number in [1,2]
Jul
26
revised $\nabla \cdot (\mathbf{B}\mathbf{B} - \frac{1}{2}B^2 \tilde{1})=(\nabla \cdot \mathbf{B})\mathbf{B} - \mathbf{B} \times (\nabla \times \mathbf{B})$
added 5 characters in body
Jul
24
answered $\sum a_n$ converges, $a_n \in \mathbb{R}$, then there exists real sequence $b_n$ such that $b_n\rightarrow +\infty$ and $\sum a_n b_n$ converges.
Jul
23
revised Prove: $x^n=0 \to x=0$
added 17 characters in body
Jul
23
comment Prove: $x^n=0 \to x=0$
You should appeal to an axiom in each of the "therefore" statements you make, or otherwise use a different approach.
Jul
23
revised Prove: $x^n=0 \to x=0$
added 102 characters in body