How to call this set? Say $I=(x_1,x_2,x_3, ..., x_n)$ where $0 \le x_i \le 1$. Then all $I$ shall forms a set.
Question is, does this kind of set have a specific name? or How will you call it with respect to the constraint  $0 \le x_i \le 1$?
Than you.

It's the cartesian product: $$I=[0,1]^n=\underbrace{[0,1]\times[0,1]\times\cdots\times[0,1]}_{\displaystyle n~\text{times}}$$ often called $n$-dimensional cube or hypercube.
