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15h
answered What is $\limsup_{n\to\infty} \frac{p_{n+1}}{p_n}$?
Aug
30
awarded  Necromancer
Aug
28
answered $a^{\log_g b} = b^{\log_g a}$?
Aug
28
comment Spaces $X$ in which every subset is either open or closed, and only $\varnothing$ and $X$ are clopen
@Ian Sorry I always forget this, by separable I mean Haussdorff...
Aug
28
comment Spaces $X$ in which every subset is either open or closed, and only $\varnothing$ and $X$ are clopen
@Ian Do you know any countable such example? Finite is clearly impossible.
Aug
28
comment Given an arbitrary sequence {$x_n$} in $\Bbb{R}$, find a test function $f$ with $f^{(n)}(0)=x_n$
If $x_n = (n!)^2$ then your series is divergent for all $x \neq 0$, so it doesn't exist.
Aug
28
answered Spaces $X$ in which every subset is either open or closed, and only $\varnothing$ and $X$ are clopen
Aug
27
answered Prove by definition that $(x,2)\subset\mathbb Z[x]$ is a maximal ideal
Aug
26
answered Evaluate $\int \theta\sec\theta \tan\theta \ d\theta$
Aug
26
comment prove that if $ h = |f_1|^2 \cdots + |f_n|^2$ is constant then $f_i$ is constant
Is $G$ a group or a set? Open where? If $G \mathbb R$ the result is not true, $f_1=\sin(x), f_2=\cos(x)$ is a counterexample....
Aug
26
answered Prove $((a+b)/2)^n\leq (a^n+b^n)/2$
Aug
25
answered Prove that If $\lim_{n \to \infty} |x_n-x_{n+p}| = 0$ for all $p \geq 1$, then $\{x_n\}$ is Cauchy sequence ???
Aug
24
answered Arithmetic and geometric sequence
Aug
23
answered How do I prove $\lVert{x}\rVert_2\leq{1}$
Aug
19
comment prove that $f'(a)=\lim_{x\rightarrow a}f'(x)$.
This is overkill and probably circular logic, but here it comes: This follows imediatelly from L'Hopital.
Aug
19
comment Let $f$ be differentiable $\exists\theta\backepsilon f(x+y)-f(x)=f '(x+\theta y)\cdot y$ Show that $\lim\limits_{y\rightarrow 0}\theta=\dfrac{1}{2}$
Note that in many cases $\theta$ is not unique, so not well defined. Also, if it is not unique, choices of $\theta$ can lead to different limits... For example, take $f$ to be a constant function....
Aug
17
awarded  Nice Answer
Aug
13
answered Prove that there is such an increasing sequence $\{k_n\}$ of positive integers
Aug
13
awarded  Nice Answer
Aug
12
answered Ring of rational 2x2 matrices has no proper ideals