Understanding Real Numbers: A Comprehensive Explanation and Examples

real numbers

Real numbers are a set of numbers that include both rational and irrational numbers

Real numbers are a set of numbers that include both rational and irrational numbers. They are called “real” numbers because they can be represented by points on a real number line. The real number line extends infinitely in both positive and negative directions.

The set of real numbers includes whole numbers (such as 0, 1, 2, 3, …), integers (including both positive and negative whole numbers), rational numbers (which can be written as fractions or terminating decimals), and irrational numbers (which cannot be written as fractions and have non-repeating decimals).

Some examples of real numbers include:

– 0
– 1
– -3
– 2/3
– -0.5
– √2 (which is an irrational number)
– π (pi, which is also an irrational number)

Real numbers can be used in various mathematical operations such as addition, subtraction, multiplication, and division. They can be compared and ordered based on their values. Real numbers also form the foundation for other number systems such as complex numbers.

It is important to note that some numbers, such as imaginary numbers (e.g., √(-1)), are not considered real numbers. However, within the set of complex numbers, real numbers are a subset.

I hope this explanation helps! Let me know if you have any further questions or need more clarification.

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