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Mar
22
comment Mapping, relations and logical expressions
What do you mean by the set $3$? Usually, one has $3 = \{0,1,2\}$, so $\alpha \subseteq 4 \times 4$...
Mar
22
comment Find $b$ such that $\log_b(x)$ and $\log_b(y)$ are integers.
@SimpleArt As both equal $b$.
Mar
22
answered Find $b$ such that $\log_b(x)$ and $\log_b(y)$ are integers.
Mar
22
answered Exercise on separable Hilbert spaces and orthonormal system
Mar
22
comment Two congruent segments does have the same length?
If I recall correctly, we define length in axiomatic geometry by taking the segments modulo congruence. That is the set of possible length is $$ L = \{\text{segments}\}/\cong $$ and the length of a particular segment is the class of it modulo congruence: Hence, obviously, by definition of length, not of congruence, your claim is true.
Mar
22
comment Prove the product of two $W_0^{1,p}$ functions gives another $W_0^{1,p}$ function if $p>n$
It is not true that $$\def\n#1{\left\|#1\right\|_{W^{1,p}}}\n{uv} \le \n u \n v $$
Mar
22
comment convolution: how can I show that $(y*f)'(t) = (y'*f)(t) + y(0)f(t)$
I did not leave off any steps and added something regarding your mistakes.
Mar
22
revised convolution: how can I show that $(y*f)'(t) = (y'*f)(t) + y(0)f(t)$
added 596 characters in body
Mar
22
reviewed Close Derivative functions.
Mar
22
reviewed Leave Open Is this function differentiable at $x=0$?
Mar
22
reviewed Leave Open is there a holomorphic function defined on a neigborhood of $0$ such that $f(\frac{1}{n})=\frac{1}{1+n}$
Mar
22
reviewed Leave Open Correlation in a series of 1s and 0s
Mar
22
reviewed Leave Open Use a proof by case to show that $\gcd (m+n,mn)-\gcd (m,n)$ is even for all integers $m$ and $n$.
Mar
22
reviewed Close Count the license plates possible with 4 letters and 2 digits
Mar
22
reviewed Close Finding the limit of the sequence $\left\{ {{a_n}} \right\}$
Mar
22
comment Finding the limit of the sequence $\left\{ {{a_n}} \right\}$
Possible duplicate of $\lim_{p\to \infty}\Vert f\Vert_{p}=\Vert f\Vert_{\infty}$?
Mar
22
reviewed Leave Open noncommutative ring with unity..
Mar
22
reviewed Leave Open a minoration of $P(X>x)$ with $X~N(0,1)$
Mar
22
comment Laplace Transform: $g(x)=a\sin(x)+\int_0^x \sin(x-u)g(u) du$
@AlexM. This integral is a convolution of functions $[0,\infty) \to \mathbf R$, for $\int_0^\infty f(t)g(x-t) \,dt$ is not well-defined for such functions, if as $g(x-t)$ only makes sense for $t \le x$. So the convolution of such functions is usually defined as $$ (f*g)(x) = \int_0^x f(t)g(x-t) \,dt $$
Mar
22
answered convolution: how can I show that $(y*f)'(t) = (y'*f)(t) + y(0)f(t)$