Chapter 2: Q16RE (page 187)
Give an example of an uncountable set.
The set of all infinite sequences of integers
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Question: Let and let for all . Show that f(x) is strictly increasing if and only if the function is strictly decreasing.
Question: a) Prove that a strictly decreasing function from R to itself is one-to-one.
b) Give an example of a decreasing function from R to itself is not one-to-one.
Question: Show that the function from the set of real numbers to the set of non-negative real numbers is not invertible, but if the domain is restricted to the set of non- negative real numbers, the resulting function is invertible.
Draw the graph of the function f (x) = [x] + [x/2] from R to R.
Show that is countable by showing that the polynomial function with is one-to-one and onto.
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