- 3

- 2

However if you add another digit (0.0 to 1.0) the answer returns nine. As you add digits the number increases. Some would say that, if you have an infinite number of digits in each number, then you can have an infinite number of numbers on the number line between 0.000... and 1.000... (beware the ellipsis). I refute this condition because, if the number has an infinite number of digits, then the last digit cannot be determined. Hence the number cannot be defined as above and cannot be positioned on the number line.

Another consequence of this definition is that the Quantum Mechanical theories of Heisenberg's uncertainty and Pauli's exclusion principles can be assigned to the number line.