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 Aug 21 comment How to see that $e^{x(1+x/3)} \le (1+x)^{(1+x)}$ for very small x>0? I think I see. Does this mean that it should be true even if I replace 3 by any fixed constant more than 2? Nov 19 comment 5 points on a plane with rational distances @MarkFischler I am sorry. I do not see why adding another point at a rational fraction between two others always works. For example, if I start with an equilateral triangle, then we cannot just add another point at a halfway between the other two, right? Nov 19 comment 5 points on a plane with rational distances @peterwhy Thank you. I will edit the question to 5 points now. Oct 29 comment A large set of low dimensional vectors in $\mathbb{F}_2^L$, which sums of any small subset do not cancel. @Servaes Sorry, I want to say that $L \le c\cdot \log n$ for some fixed $c$. Oct 29 comment A large set of low dimensional vectors in $\mathbb{F}_2^L$, which sums of any small subset do not cancel. @JyrkiLahtonen Thank you. I change it to $\mathbb{F}_2^L$ now. Oct 29 comment A large set of low dimensional vectors in $\mathbb{F}_2^L$, which sums of any small subset do not cancel. @Servaes Thank you. I tried to fix my mistake. Dec 17 comment Insightful proofs for Sherman-Morrison Formula and Matrix Determinant Lemma Oh, by looking at the spectrum of $I+\mathbf{u}\mathbf{v}^T$, we have the nice proof for Matrix Determinant Lemma as well. Dec 17 comment Insightful proofs for Sherman-Morrison Formula and Matrix Determinant Lemma This gives very good explanation. But could you explain more why only $I +\mathbf{u}g\mathbf{v}^T$ satisfies such a spectrum ?