Chapter 2: Q14E (page 115)
Question: Determine whether is onto if
Answer:
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Question: a) Prove that a strictly increasing function from R to itself is one-to-one.
b) Give an example of an increasing function from R to itself is not one-to-one.
Show that the set of odd integers is countable
a) define , the cardinality of the set S.
b) Give a formula for , where A and B are sets.
Show that when you substitute for each occurrence of n and for each occurrence of m in the right-hand side of the formula for the function in Exercise 31 , you obtain a one-to-one polynomial function . It is an open question whether there is a one-to-one polynomial function .
a) define the union, intersection, difference, and symmetric difference of two sets.
b) What are the union, intersection, difference, and symmetric difference of the set of positive integers and the set of odd integers?
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