Set of Integers

The set of integers, denoted as , includes all positive and negative whole numbers, along with zero. For example, the numbers , , and are all integers. In contrast, numbers like or , which are not whole numbers, are not part of the set of integers.

Here’s a representation of the set of integers:

Integers can be categorized further into positive integers (natural numbers), negative integers, and zero. Positive integers are greater than zero, negative integers are less than zero, and zero is neither positive nor negative.

Set of Natural Numbers

The set of natural numbers, denoted as ℕ, includes all positive integers starting from 0. In some definitions, the set starts from 1 instead of 0.

Set of Rational Numbers

The set of rational numbers, denoted as ℚ, can be defined by the quotient of two numbers belonging to the set of integers, where the divisor is non-zero.

Set of Real Numbers

The set of real numbers, denoted as ℝ, includes all rational and irrational numbers. It represents the entire continuum of possible number values from negative infinity to positive infinity.