I was wondering how to write vector notation with an index which is not included in the vector. In sets we can write,
$$ A=\{0,1,2,3,4\},$$
then if we don't want to include the element $\{0\}$ we can write,
$$A \setminus \{0\}=\{1,2,3,4\}.$$
Is there a way to write that for a vector?
i.e. for vector $a=(a_0,a_1,a_2,a_3,a_4)$ can we write $a\setminus a_0=(a_1,a_2,a_3,a_4)$?
Thank you very much.
There is a way to do this, but it's not convenient or useful. However, I thought I'd share it.
Consider the vector $a=(a_0,a_1,a_2)$. What is this vector? It's a set of ordered pairs. Specificially, this vector in $\mathbb{R}^3$ is defined as $\left\{(0,a_0),(1,a_1),(2,a_2)\right\}$. Let's suppose we wanted the vector $(a_0,a_1)\in\mathbb{R}^2$. We could write this vector as $a \setminus (2,a_2)$.
No one really thinks of vectors as sets as I've described, so it'd be confusing for almost everybody, but it can be done. :)