An abstract bit is an element of the set , which has two elements. An abstract bit is to $B$ as a number is to $N$ . The set $N$ contains a bunch of "numbers", and these numbers sometimes have many different labels, such as "three" and "3". Similarly, the set $B$ contains a pair of "bits", which sometimes have many different labels. The abstract bits are sometimes labeled 0 and 1; true and false; yes and no; or + and -. The labels don't matter; the point is that the set $B$ contains two elements, and we call those elements (abstract) bits.

Bit (abstract)