Consider the following statements about natural numbers: (1) There exists a smallest natural number. (2) There exists a largest natural number. (3) Between two natural numbers, there is always a natural number. Which of the above statements is/are correct?

### Concept & Logic Analyze the fundamental properties of the set of Natural Numbers, denoted mathematically as $\mathbb{N} = \{1, 2, 3, \dots\}$. ### Step-by-Step Solution **Deduction:** 1. Statement (1): The set of natural numbers begins at $1$. Therefore, $1$ is the smallest natural number. This statement is **True**. 2. Statement (2): Natural numbers extend infinitely upward. For any number $n$, there is always $n+1$. There is no largest natural number. This statement is **False**. 3. Statement (3): Consider two consecutive natural numbers like $1$ and $2$. There are no integer or natural values between them. This statement is **False**. 4. Consequently, only the first statement is correct. ### Exam Strategy & Shortcut To quickly falsify broad mathematical statements, search for a single basic counterexample. For statement 3, simply pick $1$ and $2$. Since there's no whole count between them, the statement immediately fails, letting you eliminate options quickly. ### Common Pitfall Students often confuse the properties of natural numbers with real or rational numbers. While it is true that there are infinite real numbers between any two real numbers, this density property does not apply to discrete, countable sets like natural numbers. ### Final Answer Therefore, the correct answer is **Only 1**.