Understanding Real Numbers: Properties and Examples

Real numbers

Real numbers are a type of mathematical quantity that includes all rational and irrational numbers

Real numbers are a type of mathematical quantity that includes all rational and irrational numbers. They represent all the possible values that can be assigned to a variable in mathematical equations.

Real numbers are often denoted by the symbol “𝑅”. They include numbers such as integers (whole numbers, both positive and negative), fractions (ratios of two integers), decimals (including terminating decimals and repeating decimals), and irrational numbers (numbers that cannot be expressed as fractions and have non-repeating decimal representations).

The set of real numbers is infinite and densely packed on the number line, meaning that there is no gap between any two real numbers. The number line extends infinitely in both the positive and negative directions.

Here are some examples of real numbers:
– Integers: -3, -2, -1, 0, 1, 2, 3
– Fractions: 1/2, -3/4, 2/5
– Decimals: 0.25, -1.75, 3.14159
– Irrational numbers: √2, π (pi), e (Euler’s number)

Real numbers are used in various branches of mathematics, such as algebra, calculus, and trigonometry, to solve equations, measure quantities, and represent real-world phenomena.

It is worth mentioning that real numbers are distinct from complex numbers, which include both real and imaginary components.

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