# Math Help - Well-Ordering Principle

1. ## Well-Ordering Principle

Show that if a and b are positive integers, then there is a smallest positive integer of the form $a - bk, \ k \in \mathbb{Z}$.

2. Originally Posted by Aryth
Show that if a and b are positive integers, then there is a smallest positive integer of the form $a - bk, \ k \in \mathbb{Z}$.
Consider the set, $S = \{a-bk > 0 | k \in \mathbb{Z} \}$
Argue that the set is non-empty and choose the smallest such natural number.

3. That was too easy, but my professor is a very nervous person and refuses to teach... Instead all of his lectures consist of the words "Uhh" and "Umm".