I am unable to get the difference between a well ordered set and a totally ordered set ,I have gone through book , it says that if some non-empty subset of a poset has a least element then it is a well-ordered set but this least element can only be found in the relation less than equal to , we can't find it in a relation like "x divides y ", so then what is the significance of the term least here ?
[Math] what is the difference between well ordered set and totally ordered set
discrete mathematics
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Best Answer
In a totally ordered set $P$, every pair of elements is comparable i.e. if we have $a,b\in P$, then $a\le b$ or $b\le a$ holds.
In contrast, a well-ordered set is a totally ordered set with an additional property that every subset $W$ of $P$ contains a smallest element $s\in W$ in the sense that for any $a\in W$ we have $s\le a$.