On 13 mar, 19:57, fom <fomJ...@nyms.net> wrote: > On 3/13/2013 9:32 AM, JT wrote: > > > The answer to why is simple, any number that can not be expressed as a > > sum of fractions is invalid > > Do you mean inadmissible? > > According to what you have said, there are > valid numbers and invalid numbers. Although > the terminology is not conventional, invalid > numbers are still numbers.
No an ivalid label is not a number thus 0.333... is not a number that can be expressed arithmeticly it is an apporximation or more likely an abberation from the standard decimal format. It was dreamt up when mathematicians realised there was really no good way to express 1/3 in binary nor decimal form (in even bases). An adhoc approach was necessary but either the mathematical skillset was missing or a lack of understanding of howto implement the necessary arithmetic circuits in machinery as in the human brain.
Althougy fractions in other bases must been understood since the old greeks. No there is no invalid numbers just numbers and malformed implementation of numerical values, they do not by any means reflect numbers.