# Sets & Venn Diagrams

## Sets

A set is a collection of things. In mathematics these are commonly number sets. Sets are expressed using curly brackets: {1,2,3,4,5,...} There are a few special number sets that are useful to know.

### Special Number Sets

Here are a few special number sets that are important to know about. Natural Numbers A double struck N is used to represent this set. Natural numbers are all whole numbers going up from 0. Integers A double struck Z is used to represent this set. Integers are all whole numbers (numbers that can be represented without fractional component). Positive Integers A double struck Z with a superscript + is used to represent this set. Positive integers are all whole numbers above 0 Rational Numbers A double struck Q is used to represent this set. Rational numbers are numbers that can be written in a whole number fractional format where the denominator is unequal to 0. They are usually all numbers that have an ending number of decimal places. Numbers such as π and e are considered irrational. Real Numbers A double struck R is used to represent this set. Real numbers are all numbers that can be placed on a number line. These include π, e and other irrational numbers. The only numbers that are not real are imaginary numbers (these originate from negative square roots which are not possible using our normal number system).

## Set Notation

Make sure you understand the table above before proceeding. There is a common format for labelling sets. This is again written in curly brackets: The notation usually always starts with x and a vertical line (value x). Then, you tend to give the range of x values. Separated by a comma after that is the set that x does or does not belong to. In the example, x is any rational number between -3 and 4. IMPORTANT!: This does not have to be the format for every set notation. You may decide to leave out the range (if there is none) or not mention which set it belongs to if it can be any number. You just have to make sure that you give all the information required so that only and all the numbers in the set are covered by the notation.

## Venn Diagrams

Venn diagrams are very useful for sorting and processing data. They allow you to visually represent sets. A Venn diagram usually looks like the on underneath. It consist of overlapping circle(s) in a box. This Venn diagram contains the sets A, B and C and which include the numbers from 1 to 9. A {1,2,3,4,7,9} B {1,3,5,8} C {2,3,7} The Venn diagram shows us in which sets the different numbers are: The numbers in the outside circles (not in the overlapping section) belong to that set only. The numbers in the three large sections where two circles overlap belong to both of these sets. The numbers in the middle (where all three circles overlap) are in all three sets. The number (6) outside of the circles is not in any of the three sets. Venn diagrams can include even more circles (or less). The more circles, the more complicated they are.

### Working with Venn Diagrams

We can use diagrams to do a lot of cool things. For example, we could name sections in the Venn diagram using the set notation we have previously learnt. Have a look at the three example underneath. The shaded region represent the expression above each Venn diagram. You can do even more complex things with Venn diagrams. However, you should have learnt the basics above and be ready to continue exploring on your own.

## Check out other Lessons

We hope your were able to learn something about sets an Venn diagrams in this lesson. Be sure to check out more data topics or browsethrough all lessons in our library.
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