What are Integers? - Definition & Examples

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  • 0:03 What are Integers?
  • 2:04 Integers and Non-Integers
  • 4:16 Groups Containing Integers
  • 4:40 Lesson Summary
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Lesson Transcript
Instructor: Erin Ryan
In this lesson, we will learn about integers - what they are and what distinguishes them from other types of numbers. We'll also take a look at a few examples of things that can or cannot be measured with integers.

What Are Integers?

There are a lot of different types of numbers in the world. Each number is different than another, yet they may share some common characteristics. To help themselves keep track of and understand the similarities and differences between numbers, mathematicians have developed a grouping system that categorizes and describes numbers based on their characteristics.

Some of the most common groups in the system are:

  • Natural numbers
  • Whole numbers
  • Integers
  • Rationals
  • Real numbers

The grouping system is very similar to the concept of grouping in geography in which things are categorized using characteristics that get more and more specific (country, state, county, city, street. . .)

Integers are a special group or category of numbers that:

  • Consist of the set of numbers: {. . .-4, -3, -2, -1, 0, 1, 2, 3, 4. . .}
  • Are all positive and negative whole numbers that do not include any fractional or decimal parts

A few things to note here:

  1. There are no fractions or decimals in any part of the numbers.
  2. Negative numbers often represent the idea of being below a standard value.
  3. Zero is an integer.
  4. Remember that categories of numbers overlap, just like categories of geography (such as country, state, county, city, street) overlap each other. For instance, a street is in a certain city, which is in a certain county, which is in a certain state. Categories of math overlap each other too.
  5. Don't let the notation throw you off. The brackets - { } - are used to write sets. This is the standard mathematical notation used when you want to list a group (or a 'set') of numbers. The ellipse (. . .) just means they go on and on forever in the same pattern. This is especially helpful when the group you are trying to represent is too big to write out in its entirety.

Examples of Integers and Non-Integers

Here are some examples of integers:

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