# Luboš Motl

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bio website motls.blogspot.com location Czech Republic age 40 member for 2 years, 11 months seen Mar 12 at 7:48 profile views 2,479

Hi, I am a string theorist and a publicist.

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 May25 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. May25 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. May25 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. May25 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. May25 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"? May25 answered The form of a solution in a linear system May25 answered Exercising divergent summations: $\lim 1-2+4-6+9-12+16-20+\ldots-\ldots$ May25 comment When $G'$/$G''$ and $G''$ both are cyclic groups $G''=Z_p$, $G'=Z_p\times Z_q$, $G'/G'' = Z_q$. ;-) May25 revised Limits in Double Integration texized formula, D in it remains incomprehsible though May25 suggested suggested edit on Limits in Double Integration May25 answered What is the formal definition of $d$, or $\partial$, in differation and integration May25 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"? May25 revised Two introductory linear algebra problems added 133 characters in body; added 86 characters in body May25 revised Two introductory linear algebra problems added 493 characters in body May25 revised Two introductory linear algebra problems added 141 characters in body; deleted 141 characters in body May25 revised Two introductory linear algebra problems added 234 characters in body May25 answered Two introductory linear algebra problems May25 revised find skew lines on a cubic surface for a parametrization added 168 characters in body May25 answered find skew lines on a cubic surface for a parametrization May24 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 $p$. ;-)