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© Sven Thommesen 2011
Math: SET THEORY and INTERVALS (Needed in Ch 2, Ch 46)
[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
halfopen interval
:
[5,8) = {5, 6, 7}
(5,8] = {6, 7, 8}
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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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 Spring '09
 Business, Topology, Metric space, Complex number, Closed set

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