To which sets of real numbers does zero belong?
Zero belongs to the set of real numbers, as it is a real number itself.
Is it natural numbers, integers, and irrational numbers?
Zero belongs to several sets of real numbers:
1. The set of whole numbers: Zero is a whole number since it is not a fraction or a decimal and can be expressed as an integer.
2. The set of integers: Zero is also an integer since it has no fractional or decimal part and can be positive, negative, or zero itself.
3. The set of rational numbers: Zero is a rational number since it can be expressed as a fraction where the numerator is zero and the denominator is any nonzero number.
4. The set of real numbers: Zero is a real number as it can be located on the number line and is neither infinity nor undefined.
In summary, zero belongs to the sets of whole numbers, integers, rational numbers, and real numbers.
The number zero belongs to several sets of real numbers. These sets include:
1. The set of natural numbers (N): This set consists of positive integers starting from 1. Since zero is not a positive integer, it is not considered a natural number.
2. The set of whole numbers (W): This set includes zero along with the natural numbers (N). It is denoted as W = {0, 1, 2, 3, ...}.
3. The set of integers (Z): This set includes all positive and negative whole numbers, as well as zero. It is denoted as Z = {..., -3, -2, -1, 0, 1, 2, 3, ...}.
4. The set of rational numbers (Q): Rational numbers are numbers that can be expressed as a fraction where the numerator and the denominator are both integers. Since zero can be expressed as 0/1, it is considered a rational number.
5. The set of real numbers (R): Real numbers include all rational and irrational numbers. Since zero is a rational number, it is also classified as a real number.
To determine which sets zero belongs to, you need to understand the definitions and properties of each set.