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Section 2.8: Problem 2 Solution »

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 .