On 31 May 2007 02:12:13 -0700, firstname.lastname@example.org wrote: > >quasi wrote: >> >> For that matter, what about the fraction 1/3? >> I'm sure you accept 1/3 as a real number. >> Do you accept 1/3 = .333... ? > >I believe 1/3 is exactly a real number. I believe any division of a >span of the number line will yield a real number. > >I do not accept 1/3 = 0.333.... I regard 0.333... as strictly less. In >my personal understanding, I could never hope to say 0.999... does not >equal one while simultaneously saying 1/3 = 0.333... so I am surprised >you would expect I might accept that as literally valid.
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.
With so many numbers lacking decimal representations, there's no point to using decimals. For one thing, even if you start with a decimal. you run into trouble as soon as you start to divide.
So all you really have is rational numbers.
You don't even have sqrt(2) or Pi. For how would you define them without using a limit process? You can't.
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.