# less than or equal!!!

• Feb 9th 2010, 12:00 PM
flower3
less than or equal!!!
If $a,b \in N$ with $a/b$ {i.e: a divides b} .prove that $a \leq b$
• Feb 9th 2010, 12:32 PM
Bruno J.
Well $b=aq$ for some $q \in \mathbb N$ (here we assume that $0 \notin \mathbb N$ or else the statement is false - take $b=0$ and $a>0$). Then $q\geq 1$ so $b=aq>a\times 1 =a$.