Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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.

share|improve this question
    
Unfortunately, I only know that $\{ T \}$ is called the truth, the whole truth, and nothing but the truth. As for $B^n$, wouldn't "Boolean lattice with $n$ atoms" work? That also captures the partial order on your set. –  Michael Joyce Oct 29 '12 at 12:48
    
Oh gosh. All of you are very helpful and I've no idea which should be choosen as the answer... –  neuron Oct 29 '12 at 13:01

2 Answers 2

up vote 2 down vote accepted

Two-element Boolean algebra, at least according to Wikipedia.

share|improve this answer
1  
B gets called the Boolean domain. "The set of truth values" will also work as a label. –  Doug Spoonwood Oct 29 '12 at 12:40
    
@Doug: There are more truth values if you consider mutli-valued logic. –  Asaf Karagila Oct 29 '12 at 12:43
    
You speak correctly. If the context of classical logic (not its formulas however) comes as clear, in other words if you've presupposed {T, F} as the domain of truth and you haven't stated it, you could say "the set of truth values". "Classical truth set" perhaps might work better. –  Doug Spoonwood Oct 29 '12 at 21:57

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 $2 = \{\emptyset, \{\emptyset\}\} = \{0,1\}$.)

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.