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I have two question could not figure out about their solutions. First, give an example of two metrics on Z that are not equivalent? Secondly, A= {a+πm a,m in Z} Is A complete with respect to usual metric on R.

thank you for everyone share their opinion.

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    Please ask one question per post, or, if you see a relationship between the questions that makes it helpful to consider them together, please point it out.2012-12-10
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    For the metric, take the usual metric and the "british rail metric" given by $d(x,x) = 0$ and $d(x,y) = |x| + |y|$ for all $x \not= y$2012-12-10

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