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Jul
15
comment Expected maximum of a sequence of i.i.d. Poissons
@user159813 No problem! It's a useful fact.
Jul
15
comment Expected maximum of a sequence of i.i.d. Poissons
@user159813 Yes. The proof is easy (and is left as an exercise at the end of the blog post you linked to).
Jul
15
comment Expected maximum of a sequence of i.i.d. Poissons
@user159813 For an integer-valued random variable, $\sum_{t=0}^{\infty} \mathrm{Pr}(X > t)= \mathbb E X$.
Jul
15
comment Expected maximum of a sequence of i.i.d. Poissons
The expectation does tend to infinity, but I'm interested in its asymptotic growth. For instance, does it grow as $\Theta(\lg n)$, $\Theta(\lg \lg n)$, etc.?
May
5
comment What is the history of the use of the term “scalene triangle”?
Terrific resource, thanks!
Nov
3
comment Three old chestnuts in elementary geometry: is there a unified perspective?
My apologies, the angle should be $\angle EDB$. Fixed.
Sep
12
comment How to calculate $\lim \limits_{n \to \infty}(1 +\frac{a}{n})^n$?
What definition do you know for $e$? Do you know the value of $\lim (1+\frac{1}{n})^n$?
Feb
22
comment If $A,B\in M(2,\mathbb{F})$ and $AB=I$, then $BA=I$
The downvote was from me. Though what you have written is mathematically correct, it does not answer the OP's question as stated.
Jan
28
comment Find members of this field.
To find -1 in $\mathbb{Z}_5$, recall that the symbol "-1" stands for the (unique) element which, when added to 1, yields zero. You only have five possibilities to check. (The problem of finding 1/3 in $\mathbb{Z}_7$ is similar.)
Jan
16
comment truth table equivalency
I believe that ~ is the "not" operator.
Nov
29
comment functional equation uniqueness $f(x^{2})= f(x)^{2} $ in $\mathbb{C}$ and $f(x)+f''(x) = 0 $ in $\mathbb{C}$
@ccc: the problem statement requires that $f$ be holomorphic.
Nov
14
comment Was it an even deal for me?
Completely changing the question after posting it (without leaving any hint that the question has changed) is considered bad form.
Sep
27
comment Why are the centers of $R$ and $\text{End}_{\text{Ab}}(R)$ isomorphic?
@Pierre-Yves Gaillard: Thanks for the suggestion. I have added the author's name. The book is part of the Graduate Studies in Mathematics series.
Sep
27
comment Why are the centers of $R$ and $\text{End}_{\text{Ab}}(R)$ isomorphic?
Well that's strange. I can't see any error in what you wrote; have I misunderstood the exercise? Here is the text exactly as it appears: "2.17. Let $R$ be a ring, and let $E = \text{End}_{\text{Ab}}(R)$ be the ring of endomorphisms of the underlying abelian group $(R, +)$. Prove that the center of $E$ is isomorphic to the center of $R$."
Aug
23
comment Prove that all even integers $n \neq 2^k$ are expressible as a sum of consecutive positive integers
$10 = 1 + 2 + 3 + 4$, $12 = 3 + 4 + 5$
Aug
16
comment Can a circle's circumference be divided into arbitrary number of equal parts using straight edge and compass only?
Very nice answer! +1
Aug
10
comment Is there a way to pick a $k$ such that $p_0p_1 + ik$ is always a product of two primes?
My point is that if $k \neq 0$, then $p_0p_1 + ik$ always has at least 3 prime factors for $i = p_0p_1$.
Aug
10
comment Is there a way to pick a $k$ such that $p_0p_1 + ik$ is always a product of two primes?
$p_0p_1+(p_0p_1)k = p_0p_1 (1 + k)$, no?
Jun
11
comment Combinatorial proof that binomial coefficients are given by alternating sums of squares?
Very nice! (characters...)
Feb
11
comment If a product of relatively prime integers is an $n$th power, then each is an $n$th power
Have you considered the prime factorizations of $a$, $b$, and $c$?