What number set does -5 belong to
-5 belongs to the set of negative numbers.
The number -5 belongs to multiple number sets, including:
1. The set of integers (Z): -5 is an integer because it is a whole number without any fractional or decimal parts. In this set, you can find all positive and negative numbers, including zero.
2. The set of real numbers (R): -5 is also a real number because it can be expressed on the number line. The set of real numbers includes all rational and irrational numbers.
3. The set of rational numbers (Q): -5 is a rational number because it can be expressed as a fraction with an integer numerator and denominator. In this set, you can find all numbers that can be represented as fractions.
4. The set of whole numbers (W): -5 is not a whole number because whole numbers include only positive integers and zero.
5. The set of natural numbers (N): -5 is not a natural number because natural numbers include only positive integers starting from 1.
To determine the number set to which -5 belongs, we first need to understand the different number sets.
1. Natural numbers (N): This set consists of positive whole numbers starting from 1 and does not include zero or negative numbers. Hence, -5 does not belong to the set of natural numbers.
2. Whole numbers (W): This set includes all the natural numbers (positive whole numbers) and zero. But, it still does not include negative numbers. Therefore, -5 does not belong to the set of whole numbers.
3. Integers (Z): This set comprises all positive and negative whole numbers, including zero. Hence, -5 does belong to the set of integers.
4. Rational numbers (Q): This set includes all numbers that can be expressed as a fraction of two integers (where the denominator is not zero). -5 can be expressed as -5/1, which is a fraction where the numerator (-5) and denominator (1) are both integers. Therefore, -5 also belongs to the set of rational numbers.
5. Real numbers (R): This set includes all rational and irrational numbers. Since -5 is a real and rational number, it belongs to the set of real numbers.
Therefore, the number set to which -5 belongs is the set of integers (Z), the set of rational numbers (Q), and the set of real numbers (R).