Limit of Modulo Operation/Limit 1
Jump to navigation
Jump to search
Theorem
Let $x$ and $y$ be real numbers.
Let $x \bmod y$ denote the modulo operation.
Then $\ds \lim_{y \mathop \to 0} x \bmod y = 0$.
Proof
By Range of Modulo Operation for Positive Modulus and Range of Modulo Operation for Negative Modulus we have:
- $-\size y < x \bmod y < \size y$
The result follows from the Squeeze Theorem for Functions.
$\blacksquare$