On Monday, October 2, 2017 at 3:15:26 AM UTC-4, John Gabriel wrote:
> > 0.999... is most accurately SHORT for the series 0.9+0.09+0.009+... > > The series 0.9+0.09+0.009+... has a limit for its partial sums which is 1. >
> Euler defined the series as being equal to its limit, that is, S = Lim S. > > There is no proof, no theorem, no other nonsense required to understand this definition. It is ill-formed concept and Euler's Blunder.
The "blunder" was actually yours, Troll Boy. The modern limit notation was not invented until several decades after Euler's death. Using that notation, we would have:
S = Lim (n --> oo): Sn = 1 (not S = Lim S)
where the partial sum Sn = Sum(k=1, n): a_k and a_k = 1 - 1/10^k
And, as you yourself were recently forced to concede when confronted with the evidence, "Of course he [Euler] did not write 'Lim S'... He did not talk about S." (May 27, 2017)
It is puzzling why you now insist on contradicting yourself again and again like this. You are looking like real psycho whack job here.