How to Classify Real Numbers

The “stack of funnels” diagram below will help us easily classify any real numbers. But first, we need to describe what kinds of elements are included in each group of numbers. A funnel represents each group or set of numbers.

this diagram shows the classification of real numbers using the idea or notion of

Description of Each Set of Real Numbers

Natural numbers (also known as counting numbers) are the numbers that we use to count. It begins with 1, then 2, 3, and so on.

<one, two, three, four, five, six, seven and so on></p>
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Whole numbers are a slight “upgrade” of the natural numbers because we simply add the element zero to the current set of natural numbers. Think of whole numbers as natural numbers together with zero.

<zero, one, two, three, four, five, six, seven and so on></p>
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Integers include all whole numbers together with the “negatives” or opposites of the natural numbers.

<negative three, negative two, negative one, zero, one, two, three and so on></p>
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Rational numbers are numbers that can be expressed as a ratio of integers. That means if we can write a given number as a fraction where the numerator and denominator are both integers; then it is a rational number.

Symbolically, we can write a rational number as:

a divided by b where a and b are integers but b is not equal to zero

Caution: The denominator cannot equal zero.

Rational numbers can also appear in decimal form. If the decimal number either terminates or repeats, then it is possible to write it as a fraction with an integer numerator and denominator. Thus, it is rational as well.

Irrational numbers are all numbers that when written in decimal form do not repeat and do not terminate. In other words, it goes on forever indefinitely without having a definite pattern.

Real numbers include both rational and irrational numbers. Remember that under the set of rational numbers, we have the subcategories or subsets of integers, whole numbers, and natural numbers.

Hierarchical Format of Real Numbers

We can also express the subsets of the set of real numbers in a hierarchical presentation. This way, we can clearly see how the different sets are related and distinct.

  1. Real Numbers [latex]\mathbb[/latex]