Definition:One
From ProofWiki
Contents |
Definition
The immediate successor element of zero in the set of natural numbers $\N$ is called one and has the symbol $1$.
Unit
The numerical quantity whose cardinality corresponds to the number one can also be called a unit.
As Euclid defined it:
- A unit is that of which each of the things that exist is called one.
(The Elements: Book VII: Definition $1$)
Also see
The existence of this element is proved in Smallest Element of Zero Complement of Naturally Ordered Semigroup.
Sources
- Seth Warner: Modern Algebra (1965): $\S 16$
