16h
comment Proving/ Disproving that a set is compact in $l^2$
Each standard unit vector, $e_i$, is in $A$. Does the sequence $(e_i)$ have a convergent subsequence?
22h
comment Uniform Convergence on every bounded closed intervals implies Uniform Convergence on $\Bbb R$
It's not true. Take $f_n=\chi_{[-n,n]}$. This converges to the constant function $1$ uniformly on any closed, bounded interval.
1d
comment Convergence from another series
$0\le(a-b)^2=a^2+b^2-2ab$.
2d
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2d
comment Continuous function rational for every point, Cantor function
It's not rational at every point.
Apr
28
comment Does convergence almost everywhere to an $L^p$ function and existence of a weakly convergent subsequence guarantee weak convergence?
Here's one way to solve your problem.
Apr
26
revised Let $f : (a,b) \rightarrow R$ and $x_{0} \in (a,b)$. Assume that there are real numbers $L$ and $M$ such that ...
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Apr
26
revised continuity of a piece wise function defined partially on a closed interval
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Apr
20
answered On the dimension of a real Normed Linear Space possessing a certain property
Apr
20
comment Why do so many projectile motion equation examples use $-16$ as the $a$ coefficient?
It's closer to $32.174$, at sea level.
Apr
19
comment On the dimension of a real Normed Linear Space possessing a certain property
In an infinite dimensional space $X$, take $Y$ to be the kernel of a discontinuous linear functional. This is dense in $X$ and proper; so, there is no $x\in X$ with $\text{dist}\,(x,Y)=1$.
Apr
17
comment How to test the convergence of $\sum^{\infty}_{n=2}\frac{1}{\ln{n}}$ and $\sum^{\infty}_{n=2}\frac{\ln{n}}{n^{1.1}}$?
$\ln n <n^{.05}$ for sufficiently large $n$.
Apr
15
comment Determine if the series converge or not
Looks an awful lot like $\root 4\of n/ n^{3/2}$ to me ...
Apr
9
comment Does the series converge or diverge? (Ratio Test)
$(2n)!\ne 2 n!$.
Apr
9
comment Integrate $\int_0^\infty x(y+x)^{n-2}dx$
Have you tried integration by parts? ($u=x$, $dv=(y+x)^{n-2}$.)
Apr
9
comment Why the tangent line is $y = f'(x_n) (x - x_n) + f(x_n)$ at $x = x_n$?
If you're on the point $(x_n,y_n)$ on a line, and you change the $x$ coordinate by $\Delta x= x-x_n$, then the $y$ coordinate changes by $\Delta y=m\Delta x$. So the new $y$ coordinate is $y=m \Delta_x+ y_n$. This is your equation.
Apr
6
comment Prob. 18, Chap. 2 in Baby Rudin: Any non-empty perfect set of real numbers which contains no rationals?
Let $I=[\sqrt2,\sqrt3]$. Remove an open interval contained in $I$ with irrational endpoints, not $\sqrt 2$, or $\sqrt 3$, that contains $r_1$. This splits $I$ into two parts. In each of the two halves, remove appropriate open sets so that $r_2$ and $r_3$ are removed (they may have already been removed, which is ok). Continue...
Apr
6
comment Prob. 18, Chap. 2 in Baby Rudin: Any non-empty perfect set of real numbers which contains no rationals?
Erm, make sure that after removing the $n$'th set, the first $n$ terms of the enumeration have been removed. You also want to start in a closed interval with irrational endpoints.
Apr
6
comment Prob. 18, Chap. 2 in Baby Rudin: Any non-empty perfect set of real numbers which contains no rationals?
Use a method similar to that of "removing middle thirds" when constructing the Cantor set. Insure the $n$'th removed set (now open intervals with irrational endpoints) contains the $n$'th term of some enumeration of the rationals.
Apr
6
revised Expressing ranges of piecewise functions where there's a break in its associated $y$-values
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