1. Give examples of sequences with the following properties. If there is no such

Question

1. Give examples of sequences with the following properties. If there is no such sequence, explain why not, citing a reference.

(a) Non-increasing, convergent.

(b) Not monotone, convergent.

(c) Not monotone, divergent.

(d) Unbounded, monotone.

(e) Bounded, increasing.

(f) Unbounded, convergent.

(g) Monotone, divergent.

(h) Decreasing, unbounded.

2.Prove that the set of prime numbers is closed in R. A prime number is a positive integer greater than 1 whose only positive integer factors are 1 and itself.

Explanation / Answer

2)

A Prime Number can be divided evenly only by 1 or itself. And it must be a whole number greater than 1.

Example: 2, 3, 5, 7, 11, etc.

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