Correct Answer - Option 3 : unbounded above in

**R**
__Concept:__

A natural number is a number that occurs commonly and obviously in nature. As such, it is a non-negative number. The set of natural numbers can be denoted by

N = {1, 2, 3, 4,....}

The set of natural numbers is bounded below and **not bounded above in R.**

We can prove not bounded above in R using contradiction.

**Proof:**

Assume by way of contradiction that N is a bounded above. Then, since N is not empty, it follows from the **completeness axiom that sup(N) exists.** Thus there must be m ∈ N such that

sup(N) - 1 < m (**sup(N) means supremum of N or least upper bound**)

⇒ sup(N) < m + 1

As m ∈ N , also **m + 1 ∈ N, Which is a contradiction.**

∴ **N is not bounded above**