I'm having a tough time trying to go through the division algorithm proof.
Theorem: Let (a,b) be two integers. Then there exists numbers q and r with a>= 0, 0=<r<=b such that a=bq+r.
In class, my professor starts the proof by using cases, but I don't really understand why he does this.
Case 1- If b>a then a=o*b+ a (0<a<b) q=0, r=a
Case 2- if b=a then a=b*1+0, q=1, r=0
Case 3- if b<a then a*1 ( I think my notes get cut off here since I was pretty confused in class).
Does anyone know where he is trying to go with this? Thanks