Chapter 2: Q18E (page 184)
Show thatis the inverse ofrole="math" localid="1668443022252" .
Since, is the inverse of .
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Draw the graph of the function f(x) = [x] + [x/2] from R to R.
Give an explicit formula for a function from the set of integers to the set of positive integers that is
Suppose that g is a function from A to B and f is a function from B to C.
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.
Prove or disprove each of these statements about the floor and ceiling functions.
a)for all real numbers x.
b)for all real numbers xand y.
c)for all real numbers x.
d)for all positive real numbers x.
e)for all real numbers xand y.
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