# Negative negligible functions

If f(n) is a negligible function, is -f(n) also negligible by definition? Since $$f(n) < \frac{1}{p(n)}$$ for all positive polynomials $p(n)$ and for some integer N such that $n > N$

Thus $$-f(n) < \frac{1}{p(n)}$$

Thanks very much in advance.

## 1 Answer

Per the standard definition, a negative quantity is always negligible. This does not matter, however, because when a definition demands that a quantity be negligible, that quantity is virtually always non-negative (e.g., a probability or an absolute value).