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Aug
6
revised Let $V$ be a vector space, $W$ a supspace. Can we conclude that $W\oplus (V/W)$ and $V$ are isomorphic?
added 2 characters in body
Aug
6
revised Let $V$ be a vector space, $W$ a supspace. Can we conclude that $W\oplus (V/W)$ and $V$ are isomorphic?
edited title
Aug
6
revised Homeomorphism between two subspaces
added 3 characters in body
Aug
6
revised Homeomorphism between two subspaces
added 3 characters in body
Aug
6
comment values of a $\displaystyle\lim_{x \to -\infty} x^a$
What is $(-\pi)^\pi$?
Aug
6
comment values of a $\displaystyle\lim_{x \to -\infty} x^a$
Your results so far are corretcd only for $a>0$. You can easily solve the remaining cases $a\in\mathbb Z\setminus\mathbb N$. How do you define $x^a$ for $x<0$ and $a\notin \mathbb Z$?
Aug
6
comment Proof About Point and Triangles
@miamiheatftw Well, ther is only one grou of four points if you have only $n=4$ points to begin with, hence the number of four-point-groups containing a triangle is trivially $\le 1$. Now if you have $k$ triangles, the claim is that the number of four-point-groups containing a triangle is $\le k(n-3)$. As $k(n-3)=k$, we have to show that the number of four-point-groups containing a triangle is $\le k$.As we already know that the number of four-point-groups containing a triangle is $\le1$, there is nothing to show for $k\ge 1$; of course there is also nothing to show for $k=0$. So all is fine.
Aug
6
comment Can a non-constant two dimensional polynomial have a set of zero points of positive measure?
Erm, so what is your question about? Non-isolated or positive measure?
Aug
6
comment Can a non-constant two dimensional polynomial have a set of zero points of positive measure?
Or try $f(x,y)=x$
Aug
6
comment Why is the argument of a complex number measured anticlockwise (from the positive real axis), rather than clockwise?
Already in traditional (planar) geometry, anti-clockwise is the "mathematically positive" direction for angles, for labelling of polygons etc. I don't see how clockwise (or anti-clockwise) should be more intuitive.
Aug
6
answered summation of a series in which each term is product of nth term of two sequence
Aug
6
comment Show that $\sqrt{2}$ is irrational using the integer root theorem
Alright, but slightly overdone I guess. The integer root theorem already says that the rational roots of $x^2-2$ are integers and divisors of $(-)2$.
Aug
6
answered Proof About Point and Triangles
Aug
6
revised Proof About Point and Triangles
added 44 characters in body
Aug
6
comment Proof About Point and Triangles
The problem statement does not rule out $k=0$ or $k>{n\choose 3}$, but in both these cases the claim is vacuously true.
Aug
5
comment In calculus, which questions can the naive ask that the learned cannot answer?
Maybe this question is its own answer?
Aug
5
answered Find a number by the decimal part of its square root
Aug
5
answered Mean and Variance of “Piecewise” Normal Distribution
Aug
5
comment Consistent Set of Sentences is Consistent in Expanded Language
There is no need to replace any symbols in axioms of $\mathcal L'$, is there?
Aug
5
answered Ways to code two arbitrary binary strings into one without loss of information, and relevant bounds