Chapter 2: Q16RE (page 187)
Give an example of an uncountable set.
The set of all infinite sequences of integers
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What is the sum of the terms of the geometric progression a+ar+...+arn when .
Draw the graph of the function f (x) = [x] + [x/2] from R to R.
Specify a codomain for each of the functions in Exercise 16. Under what conditions is each of these functions with the codomain you specified onto?
a) Define what it means for a function from the set of positive integers
to the set of positive integers to be one-to-one
b) Define what it means for a function from the set of positive integers to the set
of positive integers to be onto.
c) Give an example of a function from the set of positive integers to the set of
positive integers that is both one-to-one and onto.
d) Give an example of a function from the set of positive integers to the set of
positive integers that is one-to-one but not onto.
e) Give an example of a function from the set of positive integers to the set of
positive integers that is not one-to-one but is onto.
f) Give an example of a function from the set of positive integers to the set of
positive integers that is neither one-to-one nor onto.
Show that matrix multiplication is not commutative.
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