Absolute Value of Integer is not less than Divisors/Corollary
Jump to navigation
Jump to search
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 $17 \ \text{(iii)}$