> So in your system, you don't have any decimal representations except > those fractions whose decimals terminate. > > In other words, in your system, sqrt(2), Pi, 1/3, 2/3, 1/7, etc all > lack decimal representations.
While the decimals for these numbers may never be exact, they become beyond accurate for our needs. The infinite nature of the decimal that would best represent these numbers makes them accurate to any inifinite level of nesting within the number line. This would in fact make them considerably well suited for the use we have for them.
> So you've regressed back to just the rationals. > > So much for the area of a circle. > > So much for the Pythagorean Theorem. > > Your system has just set mathematics back a few thousand years.
I do not share you perception or observation that any such thing has occured.