Is there a name for the set containing the two Boolean values, i.e. $\{T,F\}$?
I am also thinking if $B = \{T,F\}$, and $B^n = \underbrace{B \times B\times B ... \times B}_n$, then is there a proper name for $B^n$? I thought of something like "Boolean n-space", but Google shows me that's not how people refer to it. I really appreciate it it someone can point me to the relevant terms and concepts.
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It's more common in mathematics to represent "truth values" as 0 and 1. The set $\{0,1\}$ is sometimes denoted just as $2$, especially by set theorists. The $n$-fold product would then be $2^n$. This notation looks confusing at first, but is usually unambiguous in context. (It also matches up with the usual construction of integers as finite ordinals, where $0 = \emptyset$, $1 = \{\emptyset\}$, and $2 = \{\emptyset, \{\emptyset\}\} = \{0,1\}$.)
Two-element Boolean algebra, at least according to Wikipedia.