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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.