A is said to be well ordered if for any nonempty subset B of A , B has a least element . What this means is that for any nonempty subset B of A , there is an element that is comparable to other elements and it will always be the lesser element. A well ordered set is linearly ordered . Let A be a well ordered set. Thus A is linearly ordered.
Section Let A be a collection of sets , i.e. A is a set whose elements are sets.
The section of a must be a subset of B , thus by our hypothesis a is an element of B which contradicts our assumption. The natural numbers are well ordered . The following are the Postulates of Peano, for the construction of the natural numbers . There is a natural number 1. 1 is not the successor of any natural number.