$\{0,1\}^n$ and $[0,1]^n$ notations Can someone please help me clarify the notations/definitions below:

Does $\{0,1\}^n$ mean a $n$-length vector consisting of $0$s and/or $1$s?

Does $[0,1]^n$ ($(0,1)^n$) mean a $n$-length vector consisting of any number between $0$ and $1$ inclusive (exclusive)?

As a related question, is there a reference web page for all such definitions/notations? Or do we just need to take note of them individually as we learn. Thanks.
The notation $\{0,1\}^n$ refers to the space of all $n$-length vectors consisting of $0$s and $1$s, while the notation $[0,1]^n$ ($(0,1)^n$) refers to the space of all $n$-length vectors consisting of real numbers between $0$ and $1$ inclusive (exclusive).

Edit: I often find wikipedia's list of mathematical symbols useful for looking up the meaning of symbols, although I'm not sure it would help with this question.
The idea is simple… The abstract set of Topology

$$\displaystyle{\prod_{i\in I}X_i=\left\{x:I\rightarrow\cup_{i\in I}X_i \vert x(i)=x_i\in X_i,\;\forall i\in I \right\}}$$

where $x$ are continuous functions. (Also, you can see the continuous function as equivalence relation with $n$-length vector)

Examples:


If $X_i=\{0,1\}, \forall i\in I$ then
$$\displaystyle{\prod_{i\in I}X_i=\{0,1\}^I}$$
$$x=(x_i)_{i\in I}\in\{0,1\}^I$$
If $X_i=[0,1], \forall i\in I$ then
$$\displaystyle{\prod_{i\in I}X_i=[0,1]^I}$$
Important case is the Cantor's set.


P.D.: Excuse my English, please.