Which list shows an accurate hierarchy of numbers sets within the real number system from largest to smallest
The list showing the accurate hierarchy of number sets within the real number system from largest to smallest is as follows:
1. Real numbers (ℝ): This set includes all rational and irrational numbers.
2. Irrational numbers (𝕀): This set includes numbers that cannot be expressed as fractions or terminating decimals.
3. Rational numbers (ℚ): This set includes all numbers that can be expressed as fractions, where the numerator and denominator are integers.
4. Integers (ℤ): This set includes all whole numbers (positive, negative, or zero) and their opposites.
5. Natural numbers (𝕄 or ℕ): This set includes all counting numbers, excluding zero.
The hierarchy of number sets within the real number system from largest to smallest is as follows:
1. Real Numbers (ℝ): This set includes all rational and irrational numbers. It is the largest number set within the real number system.
2. Irrational Numbers (𝕀): This set consists of numbers that cannot be expressed as a fraction or a ratio of integers. Examples include numbers like π (pi), √2 (square root of 2), and e (Euler's number).
3. Rational Numbers (ℚ): This set includes numbers that can be expressed as a fraction or a ratio of integers. It includes whole numbers, integers, and fractions such as -2, 0, 3/4, and 5.
4. Integers (ℤ): This set includes whole numbers (both positive and negative) and zero, but not fractions or decimals. Examples include -3, -2, -1, 0, 1, 2, 3, and so on.
5. Whole Numbers (ℕ): This set includes all positive integers starting from zero. Examples include 0, 1, 2, 3, and so on.
Note: The natural numbers (ℕ) are sometimes considered separate from the whole numbers (ℕ) and are defined as the set of positive integers (1, 2, 3, ...). However, there are different conventions regarding this distinction, and some sources may include zero in the set of natural numbers as well.