Definition: Natural numbers

Natural numbers are a set of positive integers that include numbers from 1 to infinity. These numbers are countable and are widely used for calculation purposes. The set of natural numbers is represented by the letter "N".

Explanation:

This image shows the set of natural numbers.

Definition: Whole numbers

Whole numbers are a set of numbers that include all the positive integers (natural numbers) along with zero. In other words, whole numbers are non-negative integers. They do not include fractions or decimal parts. The whole numbers are denoted by the symbol "ℤ+" or simply "W".

Explanation:

This image shows the set of whole numbers.

Definition: Integers

Integers are whole numbers without fractional or decimal parts, including all positive numbers, all negative numbers, and zero. They are represented by the symbol "ℤ".

Explanation:

This image displays the integers placed on a number line.

Definition: Rational numbers

Rational numbers can be expressed as a quotient or fraction of two integers, where the denominator is not zero. In simpler terms, a rational number is any number that can be represented as a \$p/q\$, where p and q are integers and q is not equal to zero. Rational numbers include integers, fractions, and decimals that either terminate or repeat.

Explanation:

This image shows examples of rational numbers.

Definition: Irrational numbers

The set of all numbers that are not rational numbers. These are numbers that cannot be written by dividing one integer by another. When we write an irrational number as a decimal, it goes on forever, without repeating itself.

Explanation:

These are examples of irrational numbers, as shown in the image.

Definition: Real numbers

Real numbers include rational and irrational numbers, such as integers, fractions, and decimals that terminate or repeat. They are represented by the symbol ℝ and can be plotted on the number line. They are essential in mathematical disciplines like algebra, calculus, and analysis.

Explanation:

These are examples of real numbers, as shown in the image.