Natural number

Natural numbers are the among most important objects in mathematics, the easiest and most universal of enumerating systems in the world. They can be easily signified using tallymarks:

𝍩𝍩𝍩𝍩𝍩𝍩𝍩𝍩𝍩𝍩𝍩𝍩𝍩𝍩𝍩

In such a system, numbers can be added/summed by concatenating the tallymarks of one number with the next. (This is an operation lost to later, positional number systems.)

An alternative system is to include the idea of “anti-tally”, taken from physics. It is understandable that this was missed before, since anti-particles are so rare in our universe.

Properties

 * Addition is commutative
 * Addition is associative
 * Each number has a successor
 * Multiplication is commutative
 * Multiplication is associate
 * There is an Identity of multiplication
 * Multiplication is Distributive over Addition (Multiplication takes precidence over Addition, by convention)