In mathematics, often at the beginning of a text book or the start of a math class, number sets are discussed. This discussion is useful for laying a groundwork for proofs and formal logic.
Natural numbers can be thought of as the “counting numbers”. They are associated with elementary mathematics and are one of the first things children are taught in school.
The set of Integers introduces the idea of negative values. And importantly it is a superset of the natural numbers, meaning that it contains every number in the set of natural numbers, and has more elements of its own, the negative numbers.
The set of Rational numbers contains all of the natural numbers as well as new values, fractions.
Real numbers build further and introduce numbers than cannot be expressed as a fraction of two integers. This type of number is often referred to as an irrational number.