Real Numbers

Real numbers are the set of all rational and irrational numbers. They include all the numbers that can be represented on the number line. Real numbers can be positive, negative, or zero. The set of real numbers is denoted by the symbol ℝ.

Types of Real Numbers

Real numbers can be classified into different types:

1. Natural Numbers (N): These are the counting numbers, starting from 1 (1, 2, 3, 4, ...).
2. Whole Numbers (W): These include all the natural numbers along with zero (0, 1, 2, 3, ...).
3. Integers (Z): Integers include all the whole numbers and their negative counterparts, along with zero (... -3, -2, -1, 0, 1, 2, 3, ...).
4. Rational Numbers (Q): These are numbers that can be expressed as a fraction of two integers, where the denominator is not zero (e.g., 1/2, -3/4, 5/1).
5. Irrational Numbers: These are numbers that cannot be expressed as a fraction of two integers. They have non-repeating, non-terminating decimal representations (e.g., √2, π).

Operations on Real Numbers

Real numbers can be operated on using the basic arithmetic operations:

• Addition (+)
• Subtraction (-)
• Multiplication (×)
• Division (÷)

These operations follow the properties of real numbers, such as the commutative, associative, and distributive properties.

Understanding real numbers is important in a wide range of mathematical concepts, including algebra, geometry, and calculus.

Overall, real numbers form the foundation of mathematical reasoning and are essential for solving a variety of mathematical problems.

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