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 Nov 19 comment Derivative of big O symbol $f(x) = O(1)$ just means that $f(x)$ is bounded near $0$. So your question just becomes, "if $f(x)$ is bounded near $0$ and $f(x)$ is analytic at $0$, then is $f'(x)$ bounded near $0$?". Nov 4 comment Equivalence relation in finite subset of $\mathbb N$ "Now, it is easy to prove that if a positive rational number squared is natural, then the rational number itself is natural." +1. This way is much better than using factorization. Nov 4 revised Equivalence relation in finite subset of $\mathbb N$ don't use . for multiplication Nov 4 answered Why don't I get $e$ when I solve $\lim_{n\to \infty}(1 + \frac{1}{n})^n$? Nov 4 comment Why don't I get $e$ when I solve $\lim_{n\to \infty}(1 + \frac{1}{n})^n$? I've found an easier way to remember it as $\log(1^\infty) = \infty\log(1) = \infty 0$ (if it were determinate, then taking the log would preserve this). Sep 18 awarded Popular Question Aug 29 comment Is it possible to put $+$ or $-$ signs in such a way that $\pm 1 \pm 2 \pm \cdots \pm 100 = 101$? Frankly, I like your proof better than any of the answers. Aug 29 answered Is there another simpler method to solve this elementary school math problem? Aug 25 comment How to prove $n!>(\frac{n}{e})^{n}$ Some of the answers at math.stackexchange.com/questions/338954/… are related to this. Aug 4 awarded Yearling Jul 25 answered How to show $\lim_{x \to 1} \frac{x + x^2 + \dots + x^n - n}{x - 1} = \frac{n(n + 1)}{2}$? Jul 25 comment How to show $\lim_{x \to 1} \frac{x + x^2 + \dots + x^n - n}{x - 1} = \frac{n(n + 1)}{2}$? You should be able to use this trick to evaluate any limit $\lim_{x\to a}\frac{f(x)}{x - a}$ (assuming $f(a) = 0$). Jul 24 comment injection $\mathbb{N}\times\mathbb{N}\to\mathbb{N}$ If $m > n$, then $\max\{m, n\}=m$, so the map is just $(m, n) \mapsto (m + n)^m$. Jul 16 revised Bound on number of zeros in smallest prime greater than $10^n$ ask another question Jul 16 comment Bound on number of zeros in smallest prime greater than $10^n$ Yeah it looks like there are quite a few more gamma.sympy.org/input/?i=nextprime%2810%5E20%29 Jul 16 asked Bound on number of zeros in smallest prime greater than $10^n$ Jun 9 comment Does the number pi have any significance besides being the ratio of a circle's diameter to its circumference? @ShreevatsaR you're just restating what $\zeta(2)$ is. That doesn't explain where the $\pi$ comes from, fundamentally. May 16 awarded Good Answer May 12 comment How to represent the floor function using mathematical notation? With the note that the $\max$ is well-defined because the set is bounded from above (by $x$), and every set of integers bounded above has a maximum element by the well-ordering principle. May 8 awarded Caucus