What is a Real Number?
A real number is any value that you can find on the continuous number line. Real numbers include both rational numbers, such as fractions and integers, and irrational numbers, such as √2 and Π. You classify real numbers into several subsets based on their properties:
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Natural Numbers: Positive integers starting from 1. Example: 1, 2, 3
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Whole Numbers: Non-negative integers starting from 0. Example: 0,1,2,3
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Integers: All whole numbers and their negative counterparts. Example: -2, -1, 0, 1, 2
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Rational Numbers: Numbers you can express as a fraction of two integers. Example: 3/4, -5, 0.5.
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Irrational Numbers: Numbers you cannot express as a simple fraction, resulting in non-terminating and non-recurring decimals. Example: √2, Π
The Geometrical Meaning of the Number Line
A real number corresponds to a unique point on the infinite number line.
When you plot numbers on a line, every point represents one and only one real number, and every real number occupies one exact location. This property means there are no gaps on the number line between real numbers.