Which list shows an accurate hierarchy of number sets within the real number system, from largest to smallest?
Responses
rational numbers, integers, whole numbers, natural numbers
rational numbers, integers, whole numbers, natural numbers - not selected, this is the correct answer
integers, rational numbers, natural numbers, whole numbers
integers, rational numbers, natural numbers, whole numbers - no response given
natural numbers, whole numbers, integers, rational numbers
natural numbers, whole numbers, integers, rational numbers - incorrect
irrational numbers, square roots, endless decimals, pi
irrational numbers, square roots, endless decimals, pi - no response given
Score
please explain
The correct answer is: rational numbers, integers, whole numbers, natural numbers.
Rational numbers include all numbers that can be expressed as a fraction, such as 1/2 or -3/4. This set is the largest, as it includes all the other number sets.
Integers are the set of numbers that include all positive and negative whole numbers, as well as zero. Examples include -3, 0, and 5.
Whole numbers are similar to integers but do not include negative numbers. So, they include all positive whole numbers and zero. Examples include 0, 1, and 10.
Natural numbers, or counting numbers, are the set of positive whole numbers. Examples include 1, 2, 3, and so on.
Therefore, the hierarchy of number sets from largest to smallest within the real number system is: rational numbers, integers, whole numbers, natural numbers.
can you make it short
it a little bot
Sure! Here's a shorter version:
The hierarchy of number sets within the real number system, from largest to smallest, is: rational numbers, integers, whole numbers, natural numbers.
The correct hierarchy of number sets within the real number system, from largest to smallest, is as follows:
1. irrational numbers
2. rational numbers
3. integers
4. whole numbers
5. natural numbers
Explanation:
- Rational numbers: These are numbers that can be expressed as a fraction, where the numerator and denominator are both integers. Examples include 1/2, -3/4, and 2/1.
- Integers: These are whole numbers (both positive and negative) including zero, as well as their negatives. Examples include -2, -1, 0, 1, and 2.
- Whole numbers: These are the non-negative integers (including zero). Examples include 0, 1, 2, 3, and so on.
- Natural numbers: These are the counting numbers or positive integers. Examples include 1, 2, 3, 4, and so on.
- Irrational numbers: These are numbers that cannot be expressed as a fraction and have an infinite non-repeating decimal representation. Examples include the square root of 2 (√2), pi (π), and the golden ratio (φ).
So, the correct hierarchy is rational numbers, integers, whole numbers, natural numbers.