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Frequently Asked
Questions
This page will contain answers to
general course related questions I may receive. Periodically take
a look at this page - it may be useful!
Question
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Answer
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Thursday, October 13 2005
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I am having problems understanding what questions 2.14 and
2.19 mean in the book. if you can please write be back i would like to
get your input.
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Question 2.14
You need to use the definition of "boundary", "region", "closed
path" and "connected component". This is not mathematical at all,
simply an explanation as to why the statement does hold - your
explanation will of course use the definitions of the terms
above. One way to approach this is to assume that the statement
does not hold (e.g., the boundary IS NOT a closed path) and argue that
this is impossible once again, using the definitions.
Question 2.19
In this question, you must also go back to the definition of a linear
operator. You are given that the median operator (as defined in
the book) is not linear so basically, to prove that it is indeed
non-linear, assume it is linear and then, using the definition of a
linear operator, provide a counter-example such that the original
assumption (e.g., that it is linear) cannot be true. For this
question, the main thing is to come up with the example. Now,
keep in mind that when sets of numbers, recall that the addition of two
sets is not the addition of the corresponding members of the set but
rather, the concatenation of the sets. For example, if you have
two sets S1 and where S1 = {0,1,2} and S2 = {3,4,5} then S1+S2 =
{0,1,2,3,4,5} and NOT {0+3, 1+4, 2+5} or {3,5,7}. So basically,
assume that the median operator is linear and then find two sets, S1
and S2 (with three members in each as in the example) where it does not
hold.
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