Search results with tag "Well ordering"

MATH 314 (SPRING 2022)

2) The ordering 6is a total well ordering, i.e., the following hold: a) For every n∈N one has: N = {m∈N |m<n}∪{n}∪{m∈N |n<m} In particular, for all m,n∈N one has: Either m6nor n6m. b) If is non-empty, there exists a unique n 0 s.t. nn 0 6n. An consequence of the above is the (generalized) Induction Principle: Theorem 0.4. Let {P n ...

  Well, Ordering, Theorem, Well ordering