Absolute Value of Integer is not less than Divisors/Corollary

Corollary to Absolute Value of Integer is not less than Divisors

Let $a, b \in \Z_{>0}$ be (strictly) positive integers.

Let $a \divides b$.

Then:

$a \le b$

Proof

Follows directly from Absolute Value of Integer is not less than Divisors.

$\blacksquare$

Sources

• 1966: Richard A. Dean: Elements of Abstract Algebra ... (previous) ... (next): $\S 0.1$. Arithmetic: Theorem $1$
• 1969: C.R.J. Clapham: Introduction to Abstract Algebra ... (previous) ... (next): Chapter $3$: The Integers: $\S 10$. Divisibility: Theorem $17 \ \text{(iii)}$