To determine the hierarchy of number sets within the real number system from largest to smallest, we need to understand the relationships between these sets. Here's an accurate hierarchy:
1. Complex Numbers: This set includes all real numbers and imaginary numbers. Complex numbers can be written in the form of a + bi, where 'a' and 'b' are real numbers, and 'i' is the imaginary unit (√(-1)).
2. Real Numbers: It includes all rational and irrational numbers. Real numbers can be represented on a number line. They include integers, fractions, decimals, and irrational numbers like π (pi) and √2 (square root of 2).
3. Rational Numbers: This set contains all numbers that can be expressed as a fraction where the numerator and denominator are integers. Rational numbers are terminating (0.75) or repeating decimals (0.333...).
4. Integers: This set consists of positive and negative whole numbers and zero (..., -3, -2, -1, 0, 1, 2, 3, ...).
5. Natural Numbers: Also known as counting numbers, this set includes positive whole numbers starting from 1 (1, 2, 3, 4, ...).
So, the hierarchy of number sets within the real number system from largest to smallest is: Complex Numbers > Real Numbers > Rational Numbers > Integers > Natural Numbers.