Match the Real Number subset to the set of numbers given. Each subset will be used. {0, 1, 2, 3, 4, 5...}
- Whole Numbers: {0, 1, 2, 3, 4, 5...}
- Natural Numbers: {1, 2, 3, 4, 5...}
- Integers: {...-4, -3, -2, -1, 0, 1, 2, 3, 4...}
- Rational Numbers: {0, 1, 2, 3, 4, 5...}
The set of numbers given is the set of natural numbers, denoted by N.
To match the Real Number subsets to the set of numbers {0, 1, 2, 3, 4, 5...}, we need to understand the different subsets of the Real Number system and identify which subset each number falls into.
The Real Number system consists of several subsets, including:
1. Natural numbers (N): These are the counting numbers that start from 1 and go on indefinitely. In this case, {0, 1, 2, 3, 4, 5...}, the set starts from 0, so it does not fall under the subset of natural numbers.
2. Whole numbers (W): Whole numbers include zero along with all the natural numbers. Since the set {0, 1, 2, 3, 4, 5...} includes zero, it falls under the subset of whole numbers.
3. Integers (Z): Integers include all the whole numbers along with their negative counterparts. Since the set {0, 1, 2, 3, 4, 5...} does not include any negative numbers, it does not fall under the subset of integers.
4. Rational numbers (Q): Rational numbers include all numbers that can be expressed as a fraction of two integers. Since the set {0, 1, 2, 3, 4, 5...} consists only of whole numbers and does not include any fractions or decimals, it does not fall under the subset of rational numbers.
5. Real numbers (R): Real numbers include all rational numbers, along with irrational numbers. Irrational numbers cannot be expressed as a fraction and have decimal representations that neither terminate nor repeat. Since the set {0, 1, 2, 3, 4, 5...} does not include any irrational numbers, it falls under the subset of real numbers.
Therefore, the set {0, 1, 2, 3, 4, 5...} matches the subset of whole numbers (W) and real numbers (R).