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Section 3.3: Problem 5 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 R. Munkres
Show that the set of sequence numbers is representable (catalog item 10).
The set of sequence numbers is where is the set of prime numbers, and is the divisibility relation. In other words, if some prime number divides , then do all prime numbers less than . This, in particular, is vacuously true for and . By catalog items 0, 3, 4 and 5, we conclude that is representable.