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May
24
comment complex analysis-roots of constant polynomial function
There is no closed-form expression for the roots of $z^{100}+z+1=w$.
May
24
comment Which one is the correct series expansion?
They are both wrong, as you will see if you take, say, $p=2$ and $n=3$.
May
24
comment distribution - exercises
Perhaps by "pair" you mean "even"? As in, $f(-x)=f(x)$?
May
24
revised Alternating series - absolute convergence?
typos
May
24
answered explaining the derivative of $x^x$
May
24
comment regular expression
What about 100?
May
24
comment weighted average
I don't know what "to get the answer distribution in percent" means.
May
24
comment confused about the limit of a trigonometric function
Much better.${}$
May
24
comment weighted average
I think you'll find that $3\times 87\ne271$. But, more to the point, you didn't say anything in your question about wanting to add the points from the different categories together. For what reason do you want to do that?
May
24
comment confused about the limit of a trigonometric function
The denominator goes to zero, but the numerator doesn't (except for certain values of $a$), so l'Hopital doesn't apply (except for those values of $a$).
May
24
comment confused about the limit of a trigonometric function
$\cot\pi$ is infinite, so for most values of $a$ the limit will not exist. But if $a$ is chosen so $\sin2\pi a=0$, maybe the limit exists.
May
24
comment Help Understanding Fields
@Andreas, you raise a valid point. Perhaps I should have phrased my answer in these terms: in characteristic 2, there are examples where $u$ and $v$ are independent, but $u+v$ and $u-v$ are dependent.
May
24
comment Is $e^x$ the only morphism for addition and multiplication?
What about $17^x$?
May
24
comment weighted average
The question is not clear to me. Certainly, you can say the average answer on category 1 is $579/108$ (the 108 comes from $9\times12$, on category 2, $450/108$, and on category 3, $87/36$. But I think you are asking for more than that.
May
24
comment How to prove the existence of solution of a non linear system of equations
Well, let's see: you can do $x=-yt/z$, so $(yt/z)^2+y^2=1$, which is $y^2(t^2+z^2)=z^2$, which becomes $y^2=z^2$, so $y=\pm z$, and then you get $x=\pm t$, shouldn't be too hard to isolate a term from there.
May
24
comment How to prove the existence of solution of a non linear system of equations
How can you prove rigorously, without plugging in any numbers or functions, that the equation $x+y=3$ has solutions (infinitely many, in fact)?
May
24
comment Prove that in two trees with same vertices there exists a vertex that the sum of its' degree in both trees is maximum $3$
It is not true that "each node has a maximum of 2 neighbours, except two that are the leaves" as a tree can have lots of vertices of very high degree. But I maintain that there is a formula for the sum of the degrees as a function of $n$. Draw a few trees with different values of $n$, add up the degrees, look for a pattern, try to prove it always holds.
May
24
answered Help Understanding Fields
May
24
comment Help Understanding Fields
Yes, characteristic 2 means $x+x=0$ for all $x$ in the field.
May
24
comment regular expression
Not quite --- your expression doesn't allow the string 0, nor the string 00.