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real analysis

Real & Complex Analysis, Calculus & Multivariate Calculus, Functional Analysis,
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Asis ghosh
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Joined: Mon Feb 05, 2018 4:22 am

real analysis

#1

Post by Asis ghosh » Sat Feb 10, 2018 5:15 pm

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*}
  1. Let $A=[-1,2]=B$. What is $A+B$?
  2. Let $A=B=\mathbb{N}$. What is $A+B$?
  3. Let $A=B=\mathbb{Z}$. What is $A+B$?
  4. Let $A=B=\mathbb{Q}$. What is $A+B$?
  5. Let $A=B=\mathbb{R}\setminus\mathbb{Q}$. What is $A+B$?
Last edited by admin on Sat Feb 10, 2018 6:53 pm, edited 1 time in total.
Reason: Replace image file with LaTeX
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