Harald Hanche-Olsen
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 21h comment inclusion-exclusion principle problem with summations Possible duplicate of Combinatorial Proof for Identity Apr 30 awarded Enlightened Apr 30 awarded Nice Answer Apr 30 comment Does every non-trivial $\mathbb{C}$-algebra contain an element which is not a square? How about the algebraic closure of the polynomial algebra? Or do you want finite-dimensional examples? Do they need to be commutative? Apr 29 comment Is it always true, for a prime $p$, a generator $g$ of $\mathbb{Z}^*_p$ cannot be a quadratic residue modulo $p$? Think about it: If $g$ is a quadratic residue then so is any power of $g$. (P.S. $p=2$ is different. You need to consider only odd primes.) Apr 26 comment $\frac{1}{z}-\frac{1}{\sin z}$ at the origin - Classify singularities The singularity is removable if and only if the function remains bounded near the singularity. It is a pole if the absolute value goes to infinity as you approach the singularity. If neither hold, it is essential. (I wonder what kind of book gives this sort of exercise without having told the students these basic facts first …) Apr 26 comment $\frac{1}{z}-\frac{1}{\sin z}$ at the origin - Classify singularities What do you know about the classification of singularities? Essential, poles, removable? Are those familiar terms? Do you know some of the basic properties of each type? Apr 26 revised $\frac{1}{z}-\frac{1}{\sin z}$ at the origin - Classify singularities Explain more Apr 26 comment $\frac{1}{z}-\frac{1}{\sin z}$ at the origin - Classify singularities My hint is very precise; can't make it more so. But if you want more hints, try to write the fractions on a common denominator. Apr 26 answered $\frac{1}{z}-\frac{1}{\sin z}$ at the origin - Classify singularities Apr 26 revised How do you split a fraction into a sum of fractions? edited tags Apr 26 answered How is the following integral rigorously meant to be understood? Apr 24 answered $A^{2014}=0$ for a matrix A Apr 18 comment the point set is nowhere dense in $X$ It is not in general true in a metric space that a singleton set is not open, nor that any point is an accumulation point. Apr 17 revised Determine the Laurent Series Oops Apr 17 answered Determine the Laurent Series Apr 17 answered Show series $\sum \frac{n^n}{(n+1)^{(n+1)}}$ diverges. Apr 12 comment Prove that $\varphi(m)+ \tau(m)\leqslant m+1$ I had to read your first sentence a few times before I realized that the missing word must be “prime” … Apr 12 answered decidable intersect undecidable Apr 11 comment Difference between $\sum_i\frac{a_i}{b_i}$ and $\frac{\sum_i a_i}{\sum_i b_i}$ @EricThoma If you assume that $\sum a_i$ and $\sum b_i$ diverge, then changing a single datum will make no difference in the limit $N\to\infty$. Your objection is probably still sound in principle, but it will take some more work to make it stick.