On Thu, 31 May 2007 18:10:51 -0700, firstname.lastname@example.org wrote: > >quasi wrote: >> >> 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.
Is sqrt(2) a real number in your system? How about Pi?
If so, how do you define them without using limits?
If not, you've already lost a lot of very useful numbers.