torstai 5. lokakuuta 2017 16.44.43 UTC+3 Markus Klyver kirjoitti: > Den torsdag 5 oktober 2017 kl. 08:01:05 UTC+2 skrev 7777777: > > torstai 5. lokakuuta 2017 8.44.17 UTC+3 Zelos Malum kirjoitti: > > > 0.999... must equal 1, there cannot be any other way for it to be. > > > > fail. > > > > in real numbers 0.(9) is not equal to 1. > > It indeed does.
> Or how do you define 0.(9)?
Using real numbers:
0.(9) = ?_(n=1 to ?)_9/10^n = ?_(n=1 to Z)_9/10^n = 0.999...999
0.999... is equal to 1 only if infinitesimals are included into the real numbers. Since the real number definition says that there are no infinitesimals in real numbers 0.999... can't be equal to 1 in real numbers, and then 0.999... = 0.999...999 = 0.(9) ? 1
You have failed to accept or understand the ambiguity of the notation 0.999... You have tried to treat it as an absolute, always equal to 1. In your absoluteness you have rejected the infinitesimals, and the infinitesimal analysis, and ended up with a dead end. You can't have rejected them and using them too, you can't eat your cake and have it too.
At the same time, you have also rejected tons of useful into that I have given, for example "my number" Z. It has led to that at the moment, you are light years behind me in doing infinitesimal analysis, and that's just because you did not come here to learn, but to win an argument, to fight against me, to fight against the truth.