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Nov
19
answered Derivative of big O symbol
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.