At the end of the day, a number is a _reification_ (or thing-a-fication, watching a process as a separate entity) of the processes of mapping and ordering. You

At the end of the day, a number is a _reification_ (or thing-a-fication, watching a process as a separate entity) of the processes of mapping and ordering. You may begin with a very simple use of those processes, which get you the natural numbers. But you may use them in more creative ways, which will get you other different classes of numbers. Mathematician love to explore all the implications of using basic processes and combining already defined numbers to create new kinds, never seen before. For example, if you start with number '1' and apply operator _successor_ (or "adding one more"), you get the *natural numbers*, which are a mapping from the size of sets to strings of operators {'1', 'successor(1)', 'successor(successor(1))', ... }. You can use this process to define an order: number A is smaller than B if you can repeatedly apply _successor_ to A and generate B in a finite time. (Not the best definition, I know, but bear with me for a second). If you reverse the _successor_ operator, you get the _predecessor_, which can be used to dismount large numbers and make them smaller. If you apply _predecessor_ to '1', you get 'predecessor(1)' which doesn't match any of the *natural* numbers as defined in the paragraph above. However, this new number is useful because you can map it to a collection without elements, allowing you to count a set of size 'zero'. This set doesn't exist, but it has a well defined size thanks to the process explained above. (You may as well apply _predecessor_ to 'zero' and count *negative numbers*, which allow you to create a mapping with debt, and thus count _I owe you_ amounts that don't exist in the physical world either). Now as for real and complex numbers, they can't count physical objects as you said because at some point you can't measure smaller and smaller magnitudes (though you can create orders with them, even if it doesn't directly involve the _successor_ operator). But mathematicians use them to count the size of _infinite sets_, which being immaterial never lose precision; you just know you can repeat their defining processes once and again, showing that there exist a mapping between any step in the process and the instance of the real or complex number that correspond to its size.