# Natural number

The most primitive method of representing a natural number is to put down a mark for each object. Later, a set of objects could be tested for equality, excess or shortage—by striking out a mark and removing an object from the set.

The addition (+) and multiplication (×) operations on natural numbers as defined above have several algebraic properties:

Even if one does not accept the axiom of infinity and therefore cannot accept that the set of all natural numbers exists, it is still possible to define any one of these sets.

**Zermelo ordinals**. Unlike von Neumann's construction, the Zermelo ordinals do not extend to infinite ordinals.