What is a number?
No matter where you look for the answer, you will probably get back a lot words—and a lot of gibberish. I, myself, am not overly fond of either gibberish or mythology.
In order to communicate with ourselves, and with others effectively, we need names—a logo.
A number is no more than a name derived through the use of an order convention designed for creating names. Simple as it is there is still today a great deal of myth as to what a number is.
The convention consists of three parts—a series of numerals one is going to use in constructing the name (number), a standard by which each thing named is going to be assigned a name, and a method by which these numerals themselves are used to construct a given name. In Arithmetic it is called Place Value Notation.
Let it be given that our numerals consist of {1, 2, 3, 4, 5, 6, 7, 8, 9, 0}
0 will be used as our place of index.
Let it be given that “Z” is our standard by which a thing is named.
Let simple Place Value Notation be the method by which a name is constructed.
Place value notation uses a one to one correspondence in a sequential manner, like thus;
zzzzzzzzzzzzzzzzzzzz
12345678901234567890
_________11111111112
etc. we read the name from bottom to top in a column.
And thus, the utility of an ordered naming convention is that by referring to the convention one can always agree as to a name.
Arithmetic is a more wholly conventionalized means of effecting a grammar system.
But what has become known as arithmetic has become corrupted by those who have never understood the meaning of convention.
Since a number is no more than a name, one can use name in place of number.
Rational Name, Whole Name, Imaginary Name, Transfinite Name—Negative Name.
If these terms sound a bit, well, insane to you, perhaps they are. Have you ever noticed how some insane people, when painting or trying to build something, over embellish it?
Since a number is no more than a name derived by the use of an ordered naming convention, can any process that use that name contradict the original convention? No—such processes and claims are made by those with little or no understanding.
And more importantly, suppose a mind resists contradiction—would the inability to learn math as taught be indicative of their failure? Or is it in fact indicative of their mental integrity?
I remember a teacher screaming at the top of her lungs at me, “You have a mental block against Learning!” because I had asked her for the third time to demonstrate to me the idea of ratio—when in fact she was demonstrating on the Blackboard simple division—a distinction one of us could not grasp.