I am studying simple concrete forms of "vector fields" $V: \mathbb{R}^n \to \mathbb{R}^n$ with some fixed $r\in\mathbb{N}$. In some texts I am reading the term "singularity" is used for the zero vector $v_z=(0,\dots,0)^T$. I find this very disturbing, because I use singularity for points in the domain where no function values are defined, which is clearly not the case here.
Can anyone tell about the usage of the terminology "singularity" especially in context with vector fields that may justify this?