Is there any formal notation for dealing with lists, rather than sets?

e.g. if I have a set $X=\{x\_1,\dots,x\_n\}$ and I want to add a new item to the set, say $x\_{n+1}$, I can say "Let $X = X \cup \{x\_{n+1}\}$" and it is clearly understood that I want to add $x\_{n+1}$ to my set.

However, if $X$ is not a set but rather a list, or tuple (i.e. the elements are ordered and duplicates are allowed), is there any way of indicating that I am adding an element to the end of the list? 

e.g. given $X=(x\_1,\dots,x\_n)$, how do I say add an element to $X$ such that $X=(x\_1,\dots,x\_n,x\_{n+1})$? i.e. how do I formally denote appending an element to $X$?
['https://math.stackexchange.com/questions/37214', 'https://math.stackexchange.com', 'https://math.stackexchange.com/users/13/']
I don't think there is any standard notation. 

One alternative would be to not use $(a,b)$ for ordered pairs but $a \times b$, which is the notation suggested by category theory. The $\times$ allows you to sweep lots of assocativity isomorphisms under the rug: it looks perfectly natural to write $(a \times b) \times c = a \times (b \times c) = a \times b \times c$, but not $((a,b),c) = (a,(b,c)) = (a,b,c)$. 

Then if you have an $n$-tuple $x$ in $X^n$, you can write $x \times a$ for the $(n+1)$-tuple in $X^{n+1}$ obtained by appending $a$.
In addition to the answers mentioned above, I would like to stress that any list can be expressed as a set. 

Formally, we can define a list to be a function, where the domain is a subset of the natural numbers. We can then express the function as a set of ordered pairs $(x,y)$, where $x$ is the input and $y$ is the output of the function.

Using this approach has the upshot that you retain *all* of the neat set notation and the reader will be familiar with the notation used in your work. On the other hand, the notation is a little (but not overwhelmingly) clunky.

As an example, if we have a list $<y\_{1},...,y\_{n}>$ of real numbers, this corresponds to a function $$f:\{1,...,n\}\rightarrow\mathbb{R},$$ where $f(1) = y\_{1}$, etc. We could then represent this list as the set $$Y =\{\hspace{3pt}(x,f(x)):x\in \{1,...,n\} \hspace{3pt}\}.$$

Consequently, to append an element to $Y$, we could consider $$Y\cup \{(n+1,y\_{n+1})\}$$

To remove the clutter from this approach, we can then slightly abuse notation by defining

$$S\cup \{y\_{n+1}\} = S\cup \{(n+1,y\_{n+1})\}.$$