Self doubt group theory

Question

Is (Z+,>=) a well oerderd set ,plz explain.

Comments

@Manoj Kumar Pandey

But the relation is >=
Z+={1,2,3,.....}

Relation(Z+,>=) is { (1,1),(2,1), (2,2), (3,1), (3,2), (3,3)........}

So the lattice/ total order form will have 1 as greatest element but no least element.

You are thinking as per the <= relation but the relation should be as per >=

:)

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Here im having a doubt that why are we considering it to be upper bounded ,what I'm thinking is like the set (3,5) exists than 3 should be the least element . Since it's >= some minimum element .

Plz correct me for this question.

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(3,5) can't be a part of the relation since 3 is not >= 5

Answer 1

Z    =set of all Integers

Z+  =set of all positive integers

A set (i.e. Z+) along with a operator (i.e. >=) is said to be well ordered set

if it satisfy the property of group as well as it has a least element(which must be constant)

Here least element is Zero.