Measurement in base 10 is not a criteria for a limit, some Q-series indeed have a limit in Q, for example:
0.333... = 1/3
Am Freitag, 6. Oktober 2017 14:57:16 UTC+2 schrieb burs...@gmail.com: > Thats the same what Markus Klyver already told you > 3 trillion times, namely Q-series need not have > a limit in Q. Here see for yourself: > > 1 + 1/2 - 1/8 + 1/16 - 5/128 + 7/256 ... = sqrt(2) > > Each partial sum is from Q, i.e. is a rational number, > their values are, all from Q, aka rational numbers: > > 1 > 1 1/2 > 1 3/8 > 1 7/16 > 1 51/128 > 1 109/256 > Etc... > > Nevertheless the limit is not from Q, since sqrt(2) > is an irrational number, or in Euclid terms an > incommensurable magnitude ratio. > > Got it? > > Question: Why do you sign your posts with "Baboon", > is this the reason you don't understand real analysis? > > Am Freitag, 6. Oktober 2017 13:36:11 UTC+2 schrieb John Gabriel: > > It applies to rational numbers that can't be measured in a given base. > > Incommensurable magnitudes cannot be measured. > > > > Baboon.