Questions: List all numbers from the given set that are: a. natural numbers, b. whole numbers, c. integers, d. rational numbers, e. irrational numbers, f. real numbers. -3, -3/7, 0, 0.1, sqrt(5), 8.4, sqrt(49) a. List all the natural numbers from the given set.

Solution Steps

To identify the natural numbers from the given set, we need to understand that natural numbers are positive integers starting from 1. We will iterate through the set and check each number to see if it is a positive integer.

The given set of numbers is \[ \left\{-3, -\frac{3}{7}, 0, 0.1, \sqrt{5}, 8.4, \sqrt{49}\right\}. \] We will analyze each element to determine which are natural numbers.

Natural numbers are defined as the set of positive integers, which can be expressed as \[ \mathbb{N} = \{1, 2, 3, \ldots\}. \]

We will check each element in the set:

• \(-3\) is not a natural number.
• \(-\frac{3}{7}\) is not a natural number.
• \(0\) is not a natural number.
• \(0.1\) is not a natural number.
• \(\sqrt{5} \approx 2.2361\) is not a natural number.
• \(8.4\) is not a natural number.
• \(\sqrt{49} = 7\) is a natural number.

From the analysis, the only natural number in the set is \(7\).

Final Answer