# Tagged Questions

Order theory deals with properties of orders, usually partial orders or quasi orders but not only those. Questions about properties of orders, general or particular, may fit into this category, as well as questions about properties of subsets and elements of an ordered set.

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### Prove that $R$ is a total order

Prove that $R$ is a total order $$R=\{(x,y)\in \mathbb{R}\times \mathbb{R}~|~ x\geq y\}$$ I just need to figure out the final portion for total order. I already have it at partial order. Thanks for ...
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### Name for a “layered” type of partial order?

I have a partial order $\prec$ over a (finite) set $S$ satisfying the following property: There exists a function $f:S\rightarrow \mathbb N$ such that $x\prec y \Leftrightarrow 0<f(x)< f(y)$....
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### Lexicographic ordering on ${\cal P}(\kappa)$

How is the "lexicographic ordering" (which is supposed to be a total ordering) on ${\cal P}(\kappa)$ defined, where $\kappa$ is any cardinal? (I apologize if this question is a bit fuzzy.)
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### Let a and b be commuting elements in a group G such as $a^m=b^n=e$. Prove that $(ab)^{mn}=e$

The problem I am working on says, "Let a and b be commuting elements in a group $G$ such that $a^m=b^n=e$. Prove that $(ab)^{mn}=e$" So what I know from this information is that ab=ba, a is an ...
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### Suppose $R$ is a partial order on $A$ and $B \subseteq A$. Prove that $R \cap (B \times B)$ a partial order on $B$.

Can somebody show me how to prove this? I would much appreciate it if one could show the givens and goals similar to how it is set out in Velleman's 'how to prove it' book, though any help would be ...
### Prove that if $(A,<)$ is a well ordering, then $(A,<)\nless(A,<)$
Prove that if $(A,<)$ is a well ordering, then $(A,<)\nless(A,<)$ I'm trying to teach myself set theory for a course I am taking and am struggling a bit here. I need to suppose for ...