Question

Which list shows an accurate heritage of number sets within the real number system from largest to smallest

Integers, rational numbers, natural numbers, whole numbers
Irrational numbers, square root, endless decimals, pi
Natural numbers, whole numbers, integers, rational numbers
Rational numbers, integers, whole numbers, natural numbers

Answer 1

The accurate heritage of number sets within the real number system from largest to smallest is:

**Rational numbers, integers, whole numbers, natural numbers.**

Here's a brief explanation of the relationships:

1. **Rational Numbers**: This set includes all fractions, which can be formed by dividing integers (e.g., -3, -1/2, 0, 1/4, 2). Rational numbers encompass both integers and whole numbers, as every integer can be expressed as a fraction (e.g., 5 = 5/1).

2. **Integers**: This set includes all whole numbers and their negative counterparts (e.g., ..., -3, -2, -1, 0, 1, 2, 3, ...).

3. **Whole Numbers**: This set is similar to integers but does not include negative numbers (0, 1, 2, 3, ...).

4. **Natural Numbers**: This set includes all positive integers starting from 1 (1, 2, 3, ...). Some definitions include 0 as a natural number, but traditionally they are regarded as starting from 1.

So, the correct order from largest set to smallest set is:
- Rational Numbers
- Integers
- Whole Numbers
- Natural Numbers