Section 8.4
239
5.
6.
(b) Recall from (a) that all numbers to the left of
x
=
7rj
are the same in
7r
and
7r'
and hence in
a.
Also, since
x
is replaced (in
7r') by the smallest number m to its right which is greater than
x,
and
the sequence of numbers following m is strictly increasing in
7r', it follows that
x
must also be
in the same position in
a
as in
7r.
But, since the sequence of integers following
x
in
7r
is strictly
decreasing and since
7r ::S
a,
it can only be that
7r
=
a.
(a) [BB] 1234
1235
1236
1245
1246
(b) 123
124
125
126
134
1256
1345
1346
1356
1456
135
136
145
146
156
2345
2346
2356
2456
3456
234
235
236
245
246
256
345
346
356
456
(a) [BB] 23459, 23467, 23468 precede; 23478, 23479, 23489 follow.
(b) 13478, 13479, 13489 precede; 13568, 13569, 13578 follow.
(c) 45678,45679,45689 precede; 46789 and 56789, the last combination in the list, follow.
7.
(a)
12
13
14
15
16
17
23
24
25
26
27
34
35
36
37
45
46
47
56
57
67
8.
(b) [BB] First list the combinations of 1, 2,
This is the end of the preview.
Sign up
to
access the rest of the document.
 Summer '10
 any
 Graph Theory, Harshad number, Self number, Order theory, Prime number, Nontotient, Monotonic function

Click to edit the document details