Show equivalence of two Cauchy sequences
Show that the Cauchy sequence .9, .99, .999,... is equivalent to 1, 1, 1...
My analysis book reads more like a novel than a math book, so unfortunately there are very few definitions, and the ones that are there are hidden in a mountian of text.
That said, I am curious about What it means to show equivalence between Cauchy sequences. I have a hunch that if I prove that they converge to the same limit, I will solve my problem. Any suggestions?