# Section 2.8: Problem 1 Solution

Working problems is a crucial part of learning mathematics. No one can learn... merely by poring over the definitions, theorems, and examples that are worked out in the text. One must work part of it out for oneself. To provide that opportunity is the purpose of the exercises.

James . Munkres

(
is dense in
.) Let
be the set of rational numbers. Show that every member of
is infinitely close to some member of
.

Let
be the relation that defines
in
(
iff
). The following sentence is true in
,
. Therefore, it is true in
. In particular, if
such that
and
, and
, then
, implying that there is
such that
. Therefore,
for every
,
, and
.