# Bit (abstract)

An ab­stract bit is an el­e­ment of the set $$\mathbb B$$, which has two el­e­ments. An ab­stract bit is to $$\mathbb B$$ as a num­ber is to $$\mathbb N$$. The set $$\mathbb N$$ con­tains a bunch of “num­bers”, and these num­bers some­times have many differ­ent la­bels, such as “three” and “3”. Similarly, the set $$\mathbb B$$ 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 $$\mathbb B$$ con­tains two el­e­ments, and we call those el­e­ments (ab­stract) bits.

Parents:

• Mathematics

Math­e­mat­ics is the study of num­bers and other ideal ob­jects that can be de­scribed by ax­ioms.

• Bit