An integer is a whole number from the set of negative, non-negative, and positive numbers. To be an integer, a number cannot be a decimal or a fraction. Here is a list of integers:
Integers are all negative and positive whole numbers, and . Integers or integer values are part of various numbering systems.
Numbering systems are ways of counting and categorizing real and imaginary objects. Integers are one set of numbers or numbering system you use every day.
Common numbering systems you may encounter include all these:
We usually write our numbers using Arabic numerals: . But we can also represent them using Roman numerals (except for ): .
Mathematicians show sets of numbers using these brackets {}, and ellipsis … to show that the numbers continue without end. So we could show a set of integers like this:
We understand that the negative numbers keep going, and so do the positive whole numbers.
Here are two different sets of numbers:
Answer – That is the set of all positive integers.
Answer – That is the set of all non-negative, even integers.
Negative integers are not whole numbers. Whole numbers are all counting numbers and . A set of integers that are not whole numbers looks like this:
A negative number that is not a decimal or fraction is an integer, but not a whole number.
Integers are positive whole numbers and their additive inverse, any non-negative whole number, and the number zero by itself. Here are examples of integers:
Non-integers are any number that is a decimal, fraction, or mixed unit. These are all not integers:
Integers pop up in most things you count each day:
Whenever you are counting real objects such as books, pencils, shoes, hats, friends, or the number of hairs on your head, you are counting with integers.
Also, every time you round a number to a whole value, you change it from a decimal, fraction or mixed unit to an integer:
Testing to see if a number is an integer is as easy as asking two questions:
Only and are integers. The other numbers are perfectly fine numbers, but they are decimals, fractions, and mixed units.
After working your way through this lesson and video, you have learned:
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