Peano zero
= Peano zero
{c}
{title2=$f(x_0+t)=o(|t|^r)$}
A Peano zero through order $r$ means that the <function> admits the zero <Taylor polynomial> with remainder $o(|t|^r)$ at $x_0$. This does not assert the existence of ordinary iterated <derivatives> on a neighborhood. For example, multiplying $t^{r+1}$ by a bounded <continuous function> with <dense> points of nondifferentiability preserves this estimate while destroying neighborhood <differentiability>.