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Jan
29
comment Solve $z^4+2z^3+3z^2+2z+1 =0$
@DylanSp it is the discriminant $b^2-4ac$ from the quadratic equation.
Jan
27
comment Some hints for “If a prime $p = n^2+5$, then $p\equiv 1\mod 10$ or $p\equiv 9\mod 10$”
Think about $n^2+5\pmod2$ and $n^2+5\pmod5$. I think this will help.
Jan
15
comment Suprema and infima in real numbers
Don't forget that squaring real numbers will make them nonnegative, so $-\infty$ is not an infimum for any of the above.
Jan
11
comment How to prove $cn < n^{\log_{2}n}$
Maybe you mean to write: for any given (but fixed!) $c$, there exists $N$ such that for all $n>N$, we have the inequality.
Jan
6
awarded  Popular Question
Jan
5
comment what is the maximum area of a cyclic pentagon?
Have you put any thought into this? Ideas, strategies, etc.? If so, what has come to mind?
Jan
1
comment Prove that $ \frac{(a-b)^2}{8a} \le \frac{a+b}{2} - \sqrt{ab} < \frac{(a-b)^2}{8b} $ when $ 0<b\le a $
@SiXUlm: Care to explain how $0<0$?
Jan
1
comment Prove that $ \frac{(a-b)^2}{8a} \le \frac{a+b}{2} - \sqrt{ab} < \frac{(a-b)^2}{8b} $ when $ 0<b\le a $
This is false when $a=b$.
Dec
31
comment Integral on a set E
It's correct. ${}$
Dec
27
comment How to get some skills to solve Topology Problems?
One thing that has always helped me in topology: come up with a concrete example and try to prove the statement for your example. Then try to abstract to a more-general setting. In this case, give an example of a $T_1$ space. Prove in that example that a singleton is a $G_\delta$ set. What properties did you use that were inherent to the topological space? If none, you have your proof written. If you used some property, how can you avoid needing it?
Dec
22
reviewed Reject and Edit Why is this a contradiction?
Dec
22
revised Why is this a contradiction?
added 10 characters in body
Dec
20
comment A sequence of zeroes of an analytic function
Won't it contain a sequence of zeroes with a limit point (namely, $1/n$ for $4\mid n$)?
Dec
20
comment Is this set in $\Bbb{C}^3$ compact?
To answer the non-highlighted question: closed and bounded is equivalent to compact in metric spaces. In the highlighted question: the set is not bounded, hence not compact as $\Bbb C^n$ is a metric space.
Dec
16
comment Functions whose second derivative is of the same sign
Starting and ending at $0$ would mean that the second derivative is nonpositive (concave down) at some points, contradicting $\psi''>0$.
Dec
10
comment How do you factor $x^2-x-1$?
Quadratic formula gives the roots, which is all you need to factor quadratic equations.
Dec
8
comment Can the existence of infinitely many even perfect numbers be settled by a diagonal argument?
I'm not sure about all of the subtleties of language differences, but I think it should actually be Euclidean @barak manos. If it is generally spelled with an 'i' in your country's English, my apologies. :-) +$1$ for the question
Dec
4
comment Sylow Subgroups small question - -shared elements of the $p$-subgroups
Nice hint: +$1$.
Dec
4
revised how to prove this type of problems?
added 27 characters in body
Dec
4
comment Explain proof by contradiction.
@5xum: I suppose it's subjective in that manner. I don't deny the connection between the statement and its contrapositive (but then again, one should see a connection among all the standard types of proof), but I would consider anything that results in a contradiction a proof by contradiction... Also, Graham Kemp's answer is identical to mine, except more succinct.