Chapter 2: Q15E (page 153)
Determine whether is onto if
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Question: Find and for the functions f and g given in exercise 36.
a) Show that if a set S has cardinality m, where m is a positive integer, then there is a one-to-one correspondence between S and the set {1,2,...m}
b) Show that if S and T are two sets each with m elements, where m is a positive integer, then there is a one-to-one correspondence between S and T.
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.
let where the domain is the set of real numbers. What is
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.
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