Search found 7 matches

by Asis ghosh
Thu Feb 22, 2018 6:12 am
Forum: Real Analysis
Topic: Real analysis
Replies: 3
Views: 5316

Re: Real analysis

please prove this question
by Asis ghosh
Mon Feb 19, 2018 10:31 am
Forum: Algebraic Structures
Topic: Classical algebra
Replies: 0
Views: 2976

Classical algebra

solve it Let $f(x) \in \mathbb{Z}[x]$ be a polynomial of degree $\geq 2$. Pick each correct statement from below: 1. If $f(x)$ is irreducible in $\mathbb{Z}[x]$ then it is irreducible in $\mathbb{Q}[x]$ . 2. If $f(x)$ is irreducible in $\mathbb{Q}[x]$ then it is irreducible in $\mathbb{Z}[x]$. 3. If...
by Asis ghosh
Wed Feb 14, 2018 5:01 pm
Forum: Analysis
Topic: Analysis
Replies: 1
Views: 3307

Analysis

solve the question

Let $f:[0, 2\pi] \rightarrow [0, 2\pi]$ be continuous such that $f(0)=f(2\pi)$. Show that there exists $x \in [0, 2\pi]$ such that

$$f(x)= f(x+\pi)$$
by Asis ghosh
Sun Feb 11, 2018 6:14 am
Forum: Algebra
Topic: abstract algebra
Replies: 0
Views: 4578

abstract algebra

Construct a group $G$ such that $G$ has a normal subgroup $N$ and $N$ has a normal subgroup $M$ (i.e. $N\vartriangleleft{G}\,,\; M\vartriangleleft{N}$), yet $M$ is not normal in $G$.
by Asis ghosh
Sat Feb 10, 2018 5:15 pm
Forum: Analysis
Topic: real analysis
Replies: 0
Views: 2884

real analysis

please solve it. Let $A,B\subset\mathbb{R}$ nonempty. Define \begin{align*} A+B:&=\big\{x\in\mathbb{R}\,|\,\exists\,(a\in{A},b\in{B})\; {\text{such that}} \, x=a+b\big\}\\ &=\big\{a+b\,|\,a\in{A},b\in{B}\big\}\,. \end{align*} Let $A=[-1,2]=B$. What is $A+B$? Let $A=B=\mathbb{N}$. What is $A+...
by Asis ghosh
Wed Feb 07, 2018 5:33 pm
Forum: Real Analysis
Topic: Real analysis
Replies: 3
Views: 5316

Real analysis

what can you say A if LUB A = GLB A ?
by Asis ghosh
Wed Feb 07, 2018 4:48 pm
Forum: Analysis
Topic: Analysis
Replies: 2
Views: 3964

Analysis

prove that (0,1) is uncountable