Paper 2, Section I, H
On the set of rational numbers, the 3 -adic metric is defined as follows: for , define and , where is the integer satisfying where is a rational number whose denominator and numerator are both prime to 3 .
(1) Show that this is indeed a metric on .
(2) Show that in , we have as while as . Let be the usual metric on . Show that neither the identity map nor its inverse is continuous.
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