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ClassNotes-Math-Sets-Intervals

# ClassNotes-Math-Sets-Intervals - Sven Thommesen 2011 Math...

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1 © Sven Thommesen 2011 Math: SET THEORY and INTERVALS (Needed in Ch 2, Ch 4-6) [Edited 09/07/10] [Read these notes after the notes on Sets.] We need some mathematical notation for describing intervals of numbers. Discrete data First we will discuss the case of intervals over natural numbers (integers). We write [a,b] when we mean “all possible values between a and b, including the values a and b”. This is called a closed interval . Thus, for natural numbers or integers, and using set notation, [0,1] = {0,1} [5,8] = {5, 6, 7, 8} We write (a,b) when we mean “all possible values between a and b, but not including the values a or b themselves”. This is called an open interval . We have: (5,8) = {6, 7} (0,1) = { } = Ø There is also the notion of a half-open interval : [5,8) = {5, 6, 7} (5,8] = {6, 7, 8}

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2 We can also use mathematical inequalities to describe our intervals. The interval [5,8] consists of all numbers that are greater than or equal to 5 and smaller than or equal to 8: x ≥ 5 and x ≤ 8 , which we can shorten to 5 ≤ x ≤ 8
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ClassNotes-Math-Sets-Intervals - Sven Thommesen 2011 Math...

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