Real numbers
the set of all rational and irrational numbers
Real numbers are a set of numbers that includes all rational and irrational numbers. In other words, any number that can be expressed as a fraction or decimal is a real number. Real numbers include positive and negative numbers, whole numbers, integers, fractions, and decimals. They are denoted by the symbol R.
Some examples of real numbers are:
– 3 (an integer)
– -2/5 (a fraction)
– 0.33 (a recurring decimal)
– √2 (an irrational number)
– π (a transcendental number)
Real numbers can be represented on a number line, where positive numbers are to the right of 0 and negative numbers are to the left. The distance between any two points on the number line is also a real number.
Real numbers are used extensively in various branches of mathematics, as well as in scientific, engineering, and financial applications. They form the foundation of calculus, algebra, geometry, probability, and many other areas of mathematics.
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