is this notation a special case of Cartesian product of two sets A and B, where A is equal to B, $\{0,1\}^2 = \{(0,0), (0,1), (1,0), (1,1)\}$?

Question

In mathematics, specifically set theory, the Cartesian product of two sets A and B, denoted A × B, is the set of all ordered pairs (a, b) where a is in A and b is in B. In terms of set-builder notation

$A\times B=\{\,(a,b)\mid a\in A\ {\mbox{ and }}\ b\in B\,\}.$

is this notation a special case of Cartesian product of two sets A and B, where A is equal to B?

$\{0,1\}^2 = \{(0,0), (0,1), (1,0), (1,1)\}$

Answer 1

Yes. In fact, you can also see this when we talk about $\mathbb{R}^2=\mathbb{R}\times\mathbb{R}$. It is a neat, compact piece of notation.