Timeline for Is $\{x_n\}$ a Cauchy sequence?

12 events

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Dec 23, 2016 at 4:37	review	Close votes
Dec 23, 2016 at 14:32
Dec 22, 2016 at 22:42	comment	added	Noam D. Elkies		Oops, make that $n - 1/2^n$ . . .
Dec 22, 2016 at 22:15	comment	added	Noam D. Elkies		@Pat Devlin (1) is vacuous (the hypothesis fails in every nonempty metric space: take $x=y$); but if you require this only for $x\neq y$ then yes it's false: let $X$ consist of the set of real numbers $a_n = n + 1/2^n$ and let $f(a_n) = a_{n+1}$.
Dec 22, 2016 at 3:30	comment	added	Isra El		$x$ is an arbitrary but fixed element in $X$ such that : ${x_n}={f^n(x)}$
Dec 21, 2016 at 8:00	answer	added	Ilya Bogdanov		timeline score: 5
S Dec 21, 2016 at 6:38	history	suggested	Amir Sagiv		changed relevant subject tags
Dec 21, 2016 at 5:35	review	Suggested edits
S Dec 21, 2016 at 6:38
Dec 21, 2016 at 5:34	comment	added	Amir Sagiv		Just for me to understand, $\{x_n\}$ is a sequence of points in $X$ given an arbitrary $x\in X$?
Dec 21, 2016 at 5:09	comment	added	Pat Devlin		Answering my own question, (2) is true, but it gives me an idea that might show (1) is false.
Dec 21, 2016 at 5:07	comment	added	Pat Devlin		Suppose we assume the weaker condition (1) that $d(f(x), f(y)) < d(x,y)$, then is it obviously false? Or if we started with the stronger assumption (2) that $d(f(x), g(x)) < d(x, y) / 1.001$, then is it obviously true?
Dec 21, 2016 at 4:30	history	edited	Arturo Magidin	CC BY-SA 3.0	spelling, grammar
Dec 21, 2016 at 4:00	history	asked	Isra El	CC BY-SA 3.0