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816
bio website motls.blogspot.com
location Czech Republic
age 40
visits member for 2 years, 11 months
seen Mar 12 at 7:48

Hi, I am a string theorist and a publicist.


May
25
comment Exercising divergent summations: $\lim 1-2+4-6+9-12+16-20+\ldots-\ldots$
But if you combine the neighbors into pairs, you may get 0+0+0... = 0, or if you single out the first 1, you get 1-0-0-0=1... The right result $1/2$ is actually the arithmetic average of these guesses, but things are usually not that simple in general.
May
25
comment Exercising divergent summations: $\lim 1-2+4-6+9-12+16-20+\ldots-\ldots$
Dear Gottfried, thanks for your interest in these matters. I would still warn you that it may be ill-advised to attribute a finite answer to any series with individual numbers. Those things may sense if there's some glimpse of a functional dependence of the terms, and even in that case one should avoid the ad hoc random clustering of the terms - this is how the convergent sums may be calculated, but that's exactly how the divergent things can't be treated. A simple example: $1-1+1-1+1-1...$ is equal to $1/2$ in any sensible definition.
May
25
comment The form of a solution in a linear system
You want to shift $\beta$ by a multiple of $1/11$, by $k/11$, that makes the absolute coefficients integer as well. $10k+7$ and $8k-1$ have to be a multiple of $11$. $k=7$ just does the job but that's not the only solution: $k=-4$ or any $11n-4$ does the job, too.
May
25
comment The form of a solution in a linear system
I see, that was my guess that this is what you wanted. Well, if you had your form only, you would first make the coefficients of $\alpha$ integer by writing $\alpha = 11\beta$ where $11$ was found as the smallest common multiple of the denominators. That would yield $(x,y,z) = (10\beta+7/11,8\beta-1/11,11\beta)$. Then you would shift $\beta$ in such a way that the absolute coefficients are also integer.
May
25
comment The form of a solution in a linear system
Apologies, I don't understand this question. What does it mean to "linearize the solution"?
May
25
answered The form of a solution in a linear system
May
25
answered Exercising divergent summations: $\lim 1-2+4-6+9-12+16-20+\ldots-\ldots$
May
25
comment When $G'$/$G''$ and $G''$ both are cyclic groups
$G''=Z_p$, $G'=Z_p\times Z_q$, $G'/G'' = Z_q$. ;-)
May
25
revised Limits in Double Integration
texized formula, D in it remains incomprehsible though
May
25
suggested suggested edit on Limits in Double Integration
May
25
answered What is the formal definition of $d$, or $\partial$, in differation and integration
May
25
comment Simple (even toy) examples for uses of Ordinals?
This sucks. I didn't know that $1+\omega$ was $\omega$. What's the purpose of such a noncommutative "addition"?
May
25
revised Two introductory linear algebra problems
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May
25
revised Two introductory linear algebra problems
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May
25
revised Two introductory linear algebra problems
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May
25
revised Two introductory linear algebra problems
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May
25
answered Two introductory linear algebra problems
May
25
revised find skew lines on a cubic surface for a parametrization
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May
25
answered find skew lines on a cubic surface for a parametrization
May
24
comment How to understand and appreciate the prime number industry?
Lowest prime whose factors are not obvious? I thought that the factors of any prime $p$ are obvious, namely $1$ and $p$. ;-)