WellOrdered.md (536B)
1 # Well Ordered 2 3 Abstract Math Chapter 10 4 5 **Definition:** A well order set has a definite smallest element. 6 7 This is important because it is the basis for [Induction](Induction.md) as without it, there would be no way to prove that $S_n\implies S_{n+1}$ means that for something is true for all values in the set. 8 9 A few examples of well ordered sets are $\N$, any known subset or provable subset of $\N$, the set {0,2,4,5646}, and infinitely many others. 10 11 Some examples of non-well ordered sets include $\R$, $\Z$, and $\mathbb{Q}$