I don't understand what is meant by the following use of little-oh.
The most obvious method to find small prime divisors of $n$ is trial division: divide $n$ by $2, 3, 5,$ etc. This takes time $y^{1 + o(1)}$ if $n$ has $y^{o(1)}$ bits. (Daniel J. Bernstein. "How to find small factors of integers." Page 2.
Here's my attempt at reading this.
Suppose $f \in o(1)$. By definition, for any $c > 0$, there's a natural number $n_0$ such that for any $n \geq n_0$, $0 \leq f < c \times 1 = c.$ (AFAIK, $c$ is a real number.) That seems to imply that $f = 0$ because that's the only thing that could be less than any $c > 0$, but that's surely not what the author is saying in his paper. What am I missing here? How should I read it? Thank you.