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 Note: Answers require pop-up windows to be enabled. Question 1 Question 2 In the diagram below place the following numbers making sure you put them in their smallest set, for example 2 goes in   which implies its then in all the others.

MATH STUDIES

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Number and Algebra

Simple Set Notation

Number sets:

The following are the different number sets you will see in the IB exams:

 This is the set of all the Natural numbers  { 0, 1, 2, 3, 4......} This is the set of integers (whole numbers positive and negative); { ...-3, -2, -1, 0, 1, 2, 3 ...} This is the set of rational numbers, that is numbers that can be written in the form where a and b and b 0 examples   -5, 0.5,  ,  100,   etc. is not a rational number. This is the set of all real numbers from negative infinity to positive infinity. It is any number that can be put on the real number line To check if it is a real number if you enter it into your calculator and press it will say NON REAL answer if not real. An example of a non real number is We can represent the above sets using a diagram: This is an example of a Venn Diagram (See Section on Sets, logic and Probability).

Other useful set definitions:

Prime numbers : This is the set of all positive integers that are divisible only by itself and 1.

Hence 1 is not a prime number.

Prime numbers = { 2,3,5,7,11......}

There are mathematicians that are constantly working on finding the largest prime number

Factors : This is a number by which another number can be divided to give a whole number answer.

Example: Factors of 12 are {1,2,3,4,6,12}

Multiples : This is best explained by giving examples.

Multiples of 3 are {3, 6, 9, 12.....}

Multiples of 5 are {5, 10, 15, 20.....}

Set Notation

The following will be used to explain and give examples of the notations above.

The letter U is normally used to represent the Universal set and letters A, B and C for example, represent subsets of the universal set.

Example : Given U =
This is another way of writing that is a natural number greater than 1 up to and including 15.

 Hence U= {2,3,4,5,6,7,8,9,10,11,12,13,14,15} A= {multiples of 3} = {3, 6, 9, 12, 15} B= {factors of 12} = {2, 3, 4, 6, 12} C= {prime numbers} = {2, 3, 5, 7, 11, 13}

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