The notion of sequence is basic notion in combinatorics and can be defined
1.Mapping from a finite set for example $$I_m=\{0,1,2,...,m-1\}$$ to an other set $X$ is finite sequence with terms in $X$ and is denote by $$s=(x_o,x_1,...,x_{m-1}), x_i\in X$$ 2.Mapping from a countable set for example $$\mathbb N=\{0,1,2,...,n,...\}$$ to an other set $X$ is infinite sequence and is denoted by $$s=(x_0,x_1,...,x_n,...), x_i\in X$$
Finite sequnces with terms from a finite set can be enumerated and they we call permutations or variations. Definition of sequences s contain two cases that are extremal.
$$s:\emptyset\to X$$ $$s:X\to\emptyset$$ $X$ is countable
How to deal with such cases. Any suggestions