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i have a relation $\mathbb{R\subseteq M\times M}$ , which is not even a partially order :

$M=\{x\epsilon\mathbb{R}$:$-3$$\leq x\leq3\}, R=\{(x,y):x>y\}$

Well what i'm trying to do; to make this relation a total order(linear order). And for this operation i can add or erase some elements as little as possible. Finally i have to give the min, max, sup, inf of the set $K\subseteq M$

Here is the set of K:


I hope you can help me!

Thanks in advance!

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Can you please clean up your question? For example, what are the sets $\mathbb R$ and $\mathbb M$? Are they the same as $R$ and $M$? Also, is this homework? If so, please add the homework tag. –  Alex Becker Jan 5 '13 at 4:30
Of course , i think i can explain. Well the relation is with "R" defined with a condition "x greater than y". "M" is the set of the relation. And "K" is the poset of "M". –  Tiro Jan 5 '13 at 4:37
No this is not a homework. This is just an exercise from a older exam of my school. And i need to solve an understand this for the preparation of my real exam.Thank you! –  Tiro Jan 5 '13 at 4:40
I get what $R$ and $M$ are. But what are $\mathbb R$ and $\mathbb M$ in the first line? You never define the blackboard versions. While I can assume $\mathbb R$ is the real numbers, I suspect this is not what you mean. –  Alex Becker Jan 5 '13 at 4:42
$\mathbb{R\subseteq M\times M}$ means that : A binary relation R is a subset of the Cartesian product of two sets A and B: –  Tiro Jan 5 '13 at 4:48

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