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 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 approved 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 added 133 characters in body; added 86 characters in body May 25 revised Two introductory linear algebra problems added 493 characters in body May 25 revised Two introductory linear algebra problems added 141 characters in body; deleted 141 characters in body May 25 revised Two introductory linear algebra problems added 234 characters in body May 25 answered Two introductory linear algebra problems May 25 revised find skew lines on a cubic surface for a parametrization added 168 characters in body 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 $p$. ;-) May 24 comment Fibration $v:S^1 \to \mathbb{R}P^1$ and a nontrivial element of $\pi_1(\mathbb{R}P^n,\ast)$ Unless there's some formal catch, I agree with @user8268. The circle $S^1$ is wrapped "twice" - from a point to the opposite point of the higher-dimensional sphere and back. This is a trivial path/submanifold both in homotopy and homology, isn't it? That's twice of the generator of the $Z_2$ group.