Number

Naturals
The most important objects in mathematics are the Natural numbers, i.e. 1, 2, 3, etc. The first way to represent these objects with a series of tallymarks:

$$IIII$$

These objects are naturally ordered, and the successor to any Natural Number is clear. We can also easily compare any numbers, such as IIIIIII and IIIIIIIIIII by pairing marks up. If they pairing has none left over, they are the same say. If there are unpaired marks, then the one with more is bigger than the other.

They can be given letter names, such as n or m or x.

Ficticious Numbers
Since the late twentieth century, mathematicians have invented many new categories of numbers, none of which hold up under scrutiny. These include
 * Real number
 * Irrational number
 * Normal number
 * Computable number