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" The moving power of mathematical invention is not reasoning but imagination. "

— Augustus De Morgan


1d
asked The existence of a normal subgroup with finite index
2d
revised Surjectiveness of standard-normal c.d.f.
added 33 characters in body
2d
asked Surjectiveness of standard-normal c.d.f.
2d
asked Fixed points of a certain type of functions with intermediate value property
2d
asked A continuous function that attains neither its minimum nor its maximum at any open interval is monotone
2d
asked Biased MLE estimate of mean (expectation)
Jul
22
comment Boundedness of a certain function defined on a closed bounded real interval
@DavidMitra: Yes , every closed bounded real interval is compact , and if a compact set is contained in the union of a collection of open sets , then it is contained in some finite sub-collection of those open sets . But I don't want to use such topological facts as the problem is not supposed to require any topology
Jul
22
comment Boundedness of a certain function defined on a closed bounded real interval
@DavidMitra: Is there any way to avoid that finite cover of compact sets ?
Jul
22
asked Boundedness of a certain function defined on a closed bounded real interval
Jul
20
asked Minima point is a solution point
Jul
17
comment To derive commutativeness of any group from the normality of all its subgroups & some other conditions
@martini:- and what about some partial converse ? can some extra restrictions be added to make the group abelian ?
Jul
17
asked To derive commutativeness of any group from the normality of all its subgroups & some other conditions
Jul
14
revised An inequality about a sequence
added 272 characters in body
Jul
11
asked An inequality about a sequence
Jul
10
accepted $\dfrac {f(x)-f(0)}{g(x)-g(0)}=\dfrac {f'\big( \theta(x)\big)}{g'\big( \theta(x)\big)}$ , $\lim_{x \to 0+} \dfrac{\theta(x)}x=?$
Jul
10
asked Is $\sin (\mathbb N)$ dense in $[-1,1]$?
Jul
9
comment $\dfrac {f(x)-f(0)}{g(x)-g(0)}=\dfrac {f'\big( \theta(x)\big)}{g'\big( \theta(x)\big)}$ , $\lim_{x \to 0+} \dfrac{\theta(x)}x=?$
how did you get $\theta(x)\big [(f^{\prime}(0)g^{\prime\prime}(b_x)-g^{\prime}(0)f^{\prime\prime}(a_x))+\frac{x‌​}{2}(f^{\prime\prime}(c_x)g^{\prime\prime}(b_x)-f^{\prime\prime}(a_x)g^{\prime\pr‌​ime}(d_x))\big ]=\frac{x}{2}(f^{\prime}(0)g^{\prime\prime}(d_x)-g^{\prime}(0)f^{\prime\prime}(c‌​_x))$ ?
Jul
9
comment $\dfrac {f(x)-f(0)}{g(x)-g(0)}=\dfrac {f'\big( \theta(x)\big)}{g'\big( \theta(x)\big)}$ , $\lim_{x \to 0+} \dfrac{\theta(x)}x=?$
but the functions you have taken doesn't satisfy $f''(0)g'(0) \ne f'(0)g''(0)$
Jul
9
revised $\dfrac {f(x)-f(0)}{g(x)-g(0)}=\dfrac {f'\big( \theta(x)\big)}{g'\big( \theta(x)\big)}$ , $\lim_{x \to 0+} \dfrac{\theta(x)}x=?$
deleted 1 character in body
Jul
9
asked $\dfrac {f(x)-f(0)}{g(x)-g(0)}=\dfrac {f'\big( \theta(x)\big)}{g'\big( \theta(x)\big)}$ , $\lim_{x \to 0+} \dfrac{\theta(x)}x=?$