# Looking for notation that extends the dimension of a vector

I am wondering if there is any notation for the following operation of a sort of concatenation of vectors. For example if I have a vector $x=(x_1,\dots,x_n)\subseteq\mathbb{F}^n$ and $y\in\mathbb{F}$ is there any notation for extending $x$ into $\mathbb{F}^{n+1}$ with the vector $(x_1,\dots,x_n,y)$? I have seen the notation $(x,y)$ given before, but these seems counter-intuitive to me I would read it as an $2$-tuple consisting of an $n$-tuple followed by a number from $\mathbb{F}$. Is there any better notation?

• I would say identification of $F^n\times F$ and $F^{n+1}$ is as obvious as it gets. If you want to make sure, mention it before using it. – Bananach Dec 6 '17 at 22:29

You could do something like $(\mathbf{x},y)$ or $(\vec{x},y)$, however you usually denote a vector. I suppose $\mathbf{x} \oplus y \in\mathbb{F}^n \oplus \mathbb F$ is okay as well, but it's clunky and really ugly/ asymmetric.
For the sake of consistency (especially if there is no reason to distinguish elements in the $n+1$-tuple), I really think $(x_1, \dots,x_n,y)$ is best for clarity, and it doesn't strike me as too cumbersome.
Assuming I'm following your question,I prefer this notation $$\left(\vec{x}_n,y\right):= (x_1,x_2,\ldots,x_n,y)$$
That's a vector arrow above $x_n$, not very visible for some reason.
The standard mathematical notation for concatenation of tuples is $$u || v$$ (see here). Thus $$(x_1,\ldots,x_n) ||y = (x_1,\ldots,x_n, y)$$