Definition talk:Convergent Sequence/Analysis

I think a word about $\epsilon$ is needed: it should be pointed from which set it is taken—then problems with $\Q$ arise (see this and that where we have values in $\Q$… joel ^talk 15:30, 29 December 2012 (UTC)

I see the problem with Rational Numbers form Metric Space which has since been corrected (silly mistake: the codomain of a metric is of course $\R$) but I can't see the problem with Definition:Absolute Value apart from the fact that it's a humongously messy page.

As for this page, I think I have corrected the obvious mistakes in it - please feel free to give it the once-over. --prime mover (talk) 15:59, 29 December 2012 (UTC)

I'm not sure how formal you are here but because absolute value for $\Q$ gives values in $\Q$ then using this function in (new) proposed definition of metric in Rational Numbers form Metric Space uses now some kind of isomorphism… is it relevant? I think this problem should be rised somewhere: there's a field in $\R$ which is isomorphic with $\Q$ etc. joel ^talk 18:40, 29 December 2012 (UTC) P.S. I heard once about ordered groups—this thing should be general enough to define there absolute value… (then it is straightforward to generalise it on ordered rings or fields etc.)