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Dec
15
comment Find the coordinate matrix of the function $\cos^2x$ relative to the ordered basis $\{1,\cos x,\sin x,\sin 2x\}$.
Since when are sets ordered?
Dec
12
comment In a fraction between integers, what denominators produce a periodic result?
Every ratio has periodic decimals, if that's what you're asking.
Dec
12
revised Defining the Complex numbers
added 296 characters in body
Dec
12
answered Defining the Complex numbers
Dec
11
answered Show that that $|\sqrt{x}-\sqrt{y}| \le \sqrt{|x-y|}$
Dec
11
comment Mind Maps for teaching Mathematics
mind maps are a waste of time in general.
Dec
11
comment Another version of Heisenberg uncertainty principle
It'd be very helpful if you could properly define all your variables.
Dec
11
comment Does $\{f_ng_n\}\to fg$ uniformly?
how can a sequence be unbounded and convergent under the natural topology?
Dec
10
comment Relatively compact subset of open set in $\mathbb{R}^n$
Ugh, this is why I secretly hate mathematics.
Dec
10
comment Relatively compact subset of open set in $\mathbb{R}^n$
@Cantor: if something is compact in $\mathbb{R}^n$, it is definitely compact in $U$. edit: ah yes, $\overline{A}$ math is simply not a subset of $U$ if it intersects the boundary.
Dec
10
comment Relatively compact subset of open set in $\mathbb{R}^n$
Isn't $A$ relatively compact because it is bounded? Just apply Heine-Borel, or am I missing something? If the coordinates of elements of $A$ are bounded by $M$, then $\overline{A}$ is bounded by $2M$.
Dec
8
comment Is $x^4+4$ an irreducible polynomial?
@Sigur: no general one, because that would probably give you an efficient algorithm for prime factorization.
Dec
8
comment Is $x^4+4$ an irreducible polynomial?
@Sigur: sometimes you can use Eisenstein's criterion, but it is generally a hard problem.
Dec
4
comment In Linear Algebra, why does the dimension of a vector space $\Bbb R ^ n $ equal $n$?
And here, my dear friends, another reason why you should not attempt to learn math from Khan.
Dec
3
comment The differentiability of $f(z)$ if $ \lim\limits_{z \to z_0} \frac {|f(z)-f(z_0)|}{|z-z_0|}=k$?
"under additional regularity assumptions".
Dec
3
comment Prime divisor in a finite group
@Mathematics123: uh... Hagen just did...
Dec
3
comment The differentiability of $f(z)$ if $ \lim\limits_{z \to z_0} \frac {|f(z)-f(z_0)|}{|z-z_0|}=k$?
You did not prove that the angle is preserved.
Dec
3
comment Prime divisor in a finite group
@Mathematics123: there are groups for which your statement is true, and there are those for which it is false.
Dec
3
comment Fields where $A^t=A$ and $A^t=-A$
I'm sorry, no, $F_2$ is the field of order 2, so just what you call $\mathbf{Z}_2$.
Dec
3
revised Fields where $A^t=A$ and $A^t=-A$
added 119 characters in body