Question

state and prove well ordering principle ​

Answer 1

Answer:

First, here is a proof of the well-ordering principle using induction:

Let S S S be a subset of the positive integers with no least element. ... Then if n + 1 ∈ S , n+1 \in S, n+1∈S, it would be the least element of S , S, S, since every integer smaller than n + 1 n+1 n+1 is in the complement of S .

Answer 2

Step-by-step explanation:

The well-ordering principle says that the positive integers are well-ordered. An ordered set is said to be well-ordered if each and every nonempty subset has a smallest or least element. So the well-ordering principle is the following statement: Every nonempty subset S S S of the positive integers has a least element.