I want to define a good notation for the number of how often the function $f:\mathbb{R}\rightarrow \mathbb{R}$ changes its sign in the interval $I\subset \mathbb{R}$ significantly.
By significantly I mean that the function changes its sign forgiven $\epsilon>0$ if there are values $x_1,x_2\in I$ with $f(x_1)>\epsilon$ and $f(x_2)<-\epsilon$.
The one notation I could think of was $ \max \{n\in\mathbb{N} :\text{there are }x_1,\ldots, x_n\in I\text{ with }x_i
However, this feels notational clumsy for such an intuitive concept. Are there better (and more standard) notations for that number?