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location Cyprus
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visits member for 2 years
seen Sep 11 at 18:50

Sep
11
comment Any open subset of $\Bbb R$ is a countable union of disjoint open intervals. [Collecting Proofs]
@user10444: It is countable yes! If you agree that $\{(\alpha_x,\beta_x):x\in U\}$ is a disjoint family of open intervals then you can see it by choosing $r_x\in \mathbb Q\cap (\alpha_x,\beta_x)$ for all $x\in U$. Then $\{r_x:x\in U\}$ is countable right? Note that the intervals $\{(\alpha_x,\beta_x):x\in U\}$ are not distinct!
Sep
11
awarded  Informed
Sep
7
awarded  Yearling
Aug
11
answered Find polynomial whose root is sum of roots of other polynomials
Aug
11
revised Generalized mean value theorem
deleted 5 characters in body
Apr
16
revised How to calculate square matrix to power n?
edited body
Apr
13
comment Why does $\gcd(a, b) = \min\lbrace ma + nb : m, n\in\mathbb{Z}\text{ and }ma+nb>0\rbrace$?
@DwayneE.Pouiller See my edited answer.
Apr
13
revised Why does $\gcd(a, b) = \min\lbrace ma + nb : m, n\in\mathbb{Z}\text{ and }ma+nb>0\rbrace$?
added 119 characters in body
Jan
26
revised Generalized mean value theorem
added 5 characters in body
Jan
11
answered Prove that if $d$ divides $n$ then $φ(d)$ divide $φ(n)$ for $φ$ denotes Euler’s φ-function.
Jan
8
comment How find this sequence $\{x_{n}\}$ such $\lim_{n\to \infty}x_{n}\left(1-\frac{n(1-na_{n})}{\ln{n}}\right)=1$
What about $x_{n}=\frac{1}{\left(1-\dfrac{n(1-na_{n})}{\ln{n}}\right)}$?
Dec
24
comment Provide a proof using the rational roots theorem
I suppose Matina Manos you mean $c$ is a positive integer!
Dec
24
revised Provide a proof using the rational roots theorem
added 7 characters in body; edited title
Dec
24
comment Number of integral roots of a polynomial
@posthumus: Since $(x-d)\mid p(x)$ it follows that $(a-d)\mid p(a)=-1$. Therefore $(a-d)\mid -1$ and similarly $(b-d)\mid -1, (c-d)\mid -1$. Also $a-d, b-d, c-d$ are $3$ different integers. Now how many factors does $-1$ have?
Dec
19
revised Find $\lim_{x\to\infty} \frac{(x+1)^2(2x-4)^3}{(2x-1)^4}$
deleted 6 characters in body
Dec
16
reviewed Leave Open Optimization using Quadratic form
Dec
16
revised Real Analysis: Unbounded Sequences
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Dec
16
revised Show that $\sum_{n=0}^\infty a_n z^n$ converges $\forall z\in\mathbb{C}.$
added 4 characters in body
Dec
15
revised Show that $\sum_{n=0}^\infty a_n z^n$ converges $\forall z\in\mathbb{C}.$
added 8 characters in body
Dec
14
reviewed Approve suggested edit on Solve $x^2\equiv 5 \pmod {35}$