as you all know, the math undergrad cultists have for some time told us that 0.999=1. Effectively the 0.999=1 meme is claiming that the sequence of partial sums 0.9,0.99,0.999... is convergent. Since a real valued sequence is convergent iff it is cauchy (Barnett 2015), I shall disprove that this sequence is cauchy to put this matter to rest. Let xn=0.99999... be a sequential term with n 9s. Let N be an arbitrary index. We take epsilon to be 0.000...001>0. now consider any indices j,k >= N. Then,

|xj-xk|=|0.999...(j times)-0.999...(k times)|
=0.000(min(j,k) times)...999...(|j-k| times)
>0.000...(max(j,k) times)...1
>epsilon

Hence 0.999... is not cauchy. I do not know why so called mathematicians still spew this propaganda. Personally I think it's an element of societal control, but feel free to discuss your own theories.