====== A B Sqrt 2 ======
==== Problem ====
Let $S$ be the set $\{a + b\sqrt{2}|a,b \in \mathbb{Q}$. Please show
  - that $S$ is a group under addition. We will denote this group $(S,+)$.
  - and that $(S,+)$ is abelian
  - that $S-{0}$ is a group under multiplication. We will denote this group as $(S-{0},*)$.
  -  

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==== Remarks ====  
  * There are more properties, I will add them later. I'm going to add all the properties of a field.

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==== $\LaTeX$ version ====
<file tex problem.a_b_sqrt_2.tex>
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% DEPENDENCIES
% RequiredPackages: \usepackage{tikz}
% RequiredMacros: \DeclareMathOperator{\aut}{Aut} 
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\begin{problem}
Type the problem code here.
\end{problem}
</file>

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==== External links ====
  * [[wp>Dihedral group]]

{{tag>problem}}