Definition:Infinite Cardinal

Definition

Let $\mathbf a$ be a cardinal.

Then $\mathbf a$ is described as infinite if and only if:

$\mathbf a = \mathbf a + \mathbf 1$

where $\mathbf 1$ is (cardinal) one.

Also see

• Definition:Infinity
• Definition:Infinite Set

Historical Note

The formulation of the concept of an infinite cardinal was evolved as a generalisation of the notion of a natural numbers as a result of the work on infinite sets by Georg Cantor.

Sources

• 1975: T.S. Blyth: Set Theory and Abstract Algebra ... (previous) ... (next): $\S 8$