Classifying Real Numbers

In this lesson, we will learn about the types of real numbers that we will encounter. Any real number can be labeled as one or more of the following: natural number, whole number, integer, rational number, or irrational number. These sets begin with the natural or counting numbers, which represent the numbers that are used when we want to count a number of objects or things. The natural numbers are the set of numbers that include all numbers starting with the number 1 and increasing by 1 out to positive infinity. Natural Numbers: {1, 2, 3, 4,…} The whole numbers are the set of natural numbers with the addition of the number 0. Whole Numbers: {0, 1, 2, 3, 4,…} The integers allow us to consider negative values. The integers are the set of whole numbers and their opposites. To the left of 0, we start counting from 1 again, but with a negative sign placed in the front of the number. Integers: {…,-3,-2,-1,0,1,2,3,…} The rational numbers are the set of all numbers that can be written as the quotient of two integers. Rational numbers written in decimal form will terminate or repeat the same pattern forever. Rational Numbers: {p/q | p and q are integers and q ≠ 0} Lastly, we have irrational numbers. Irrational numbers are real numbers that are not rational. They can’t be written as the quotient of two integers. Irrational numbers written in decimal form will not terminate nor repeat the same pattern forever. Irrational Numbers: {x | x is a real number and is not a rational number}