  # Math Integers

So what exactly are math integers? The easiest answer is that an integer is a whole number - not a fraction or a decimal. There are a few technicalities that we need to sort through, such as the fact that integers can be positive or negative, but you get the basic idea.

 Here are some example and counterexamples of integers: Integers 0, 4, 37, -12, -91 Non-integers 2.5, 1/2, -5.25, 0.13 If you are like most students, you probably prefer integers to non-integers!

Integers often are given the symbol Z. You are probably asking yourself, why isn't the symbol I? That's a good question - the answer is that is used to represent the Imaginary Numbers.

 Integers: Formal Definition

A math integer is a number in the set of positive whole numbers, negative whole numbers, or zero.

Integers are often written like this: {..., -3, -2, -1, 0, 1, 2, 3, ...}

The "..." at the beginning and end of the set means that the pattern continues forever. That means that numbers like -3,452 and 10,581 are both still integers!

 Dictionary.com definition of integer Mathematics. One of the positive or negative numbers 1, 2, 3, etc., or zero. A complete entity. Synonyms: integral, whole.

 Tricky Questions: Is it an integer?
 By this point you probably understand the definition of an integer, but there may be some situations where it could be a little confusing. Here's an example: Question: Is 10/2 is an integer? Answer: Yes! 10/2 is an integer because it can be simplified to the whole number 5. Simplifying the fraction is an important first step for determining math integers.

Before determining if your number is an integer or not, always simplify first! Even if the number is shown as a fraction and it can reduce to whole a number that means it is still an integer.

 Other Number Sets

Integers aren't the only number sets you will face in your math career. Here are a few others to consider.

 Whole Numbers(W) Whole numbers are like integers except they don't include the negative numbers. Said simpler, they are all the numbers starting at 0 and counting up Set: {0, 1, 2, 3, ...} Examples: 5, 28, 386 Natural Numbers (N) Natural numbers are also sometimes called the "Counting Number" because they the numbers you would typically count. They are exactly the same as the whole numbers with one exception: they do not include zero. Set: {1, 2, 3, 4, ...} Examples: 5, 206, 1,852 Integers (Z) I think we covered math integers above! Rational Numbers (Q) Rational numbers are any number that can be written as a fraction. Essentially this includes all of the "normal" numbers besides pi and square (or cube, etc..) roots. Examples: 5/12, 1.2645, 322 Irrational Numbers (None) Irrational numbers are all of the real numbers that are not rational. Mostly this includes pi and radicals Examples: π, √2, √7, -√10

Real Numbers (R)
Real numbers are the set of all numbers that are not imaginary! All of the number sets above are part of the real numbers.

 Imaginary Numbers (I) Imaginary numbers come when you have a negative number under the square root symbol. You probably won't learn about imaginary numbers until algebra II.

Complex Numbers (C)
Complex numbers contain both a real and imaginary number