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# Examples of Well Orders

TOPO-1XZNYW

Which of the followings are well orders?

Select ALL that apply.

A

$\leq$ on $\mathbb{Q}$.

B

$\preceq_1$ on $\mathbb{Q}$, where $p/q\preceq_1 p'/q'$ iff $q < q'$ or $q = q'$ and $p < p'$. Here $p,p'\in\mathbb{Z}$, $q,q'\in\mathbb{N}$, and $gcd(p,q)=gcd(p',q')=1$.

C

$\preceq_2$ on $\mathbb{Q}$, where $p/q\preceq_2 p'/q'$ iff $|p|+|q|<|p'|+|q'|$ or $|p|+|q|=|p'|+|q'|$ and $p/q\preceq_1 p'/q'$. Here $p,p'\in\mathbb{Z}$, $q,q'\in\mathbb{N}$, and $gcd(p,q)=gcd(p',q')=1$.

D

$\leq$ on a finite subset of $\mathbb{R}$.