Section 7: Problem 3 Solution
Working problems is a crucial part of learning mathematics. No one can learn topology 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 R. Munkres
Let
be the two-element set
. Show there is a bijective correspondence between the set
and the cartesian product
.
Similar to Exercise 6(a) of §6, i.e., given a subset of positive integers, we construct the sequence of
’s and
’s indicating for each positive integer number whether it is in the subset or not. The function is clearly injective and surjective.