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X X
X
A n, A
{1, 2, . . . , n}.
A = n.
{1, 2, . . . , m} {1, 2, . . . , n} m = n.
A
N ! A
A
A B
A N f : N ! B
C f
C = f(2N).
(A \ B) *" C " A (A \ B) *" C = A f(1) " A f(1) 8" (A \ B) *" C
8
(A \ B) *" C A. g : A ! (A \ B) *" C
{
a, a " A \ B,
" a " A : g(a) =
( )
f 2f-1(a) , a " B.
g
N
A B
A B
N " n ! f(n) " A,
m,
{1, . . . , m} " n ! g(n) " B.
f A *" B, f
N ! A *" B.
2f-1(a) + 1, a " A,
h(a) =
ó
2g-1(a), a " B
A B
A *" B ! N.
A, B f
g
N " n ! g(n) " B.
(n+1)
f n " 2N + 1,
2
H(n) =
(n)
ó
g n " 2N,
2
A
B, N ! A *" B.
A
N " n ! a(n) a" an " A.
A N " n ! an " A.
A
A B
A B
(am)m"N = (a1, a2, . . .) A
(bn)n"N = (b1, b2, . . .) B.
A B k- k = 2, 3, 4, . . .
'am, bn' m + n = k. k = 2
'a1, b2', k = 3 'a1, b2' 'a2, b1'
am.
k = 5
'a1, b4', 'a2, b3', 'a3, b2', 'a4, b1'.
A B k = 2,
k = 3, k = 4
A B,
A B
A = N *" {0}. N " N ! n - 1 " A A
B = {-1, -2, . . .} = -N N " N ! -n " B
N B. Z = A *" B
Z = N.
m
q " Q q = , m n
n
m
Q " q = ! h(q) = 'm, n' " Z Z
n
Z Z
Z Z " 'm, n' ! f('m, n') " N.
f % g : Q ! N
n
N " n ! h(n) = " Q
1
f % g h
(an)n"N = (a1, a2, . . .).
[p1, q1], [p2, q2], [p3, q3], . . .
n = 1, 2, 3, . . . :
1
qn - pn = ,
3n
[pn, qn] " [pn-1, qn-1],
a1, a2, . . . , an 8" [p2, qn].
1 2
[p1, q1] [0, ], [1, ], [2, 1]
3 3 3 3
a1.
1
[p2, q2] [p1, q1]
9
a2 a1
"
)"
{c} = [pn, qn]
n=1
c = lim pn = lim qn.
n! " n! "
n
an 8" [pn, qn] '" c " [pn, qn] ! c = an.
8
c (an)n"N
{0, 1}X X
{0, 1} P (X) X.
A " P (X) fA " {0, 1}X
1, gdy x " A,
X " x ! fA(x) =
ó
0, gdy x 8" A.
{0, 1}X P (X).
X X
" (A " P (X)) " (a " X) : A = f(a).
Z " X x " X,
f(x) :
x " Z ! x 8" f(x). (")
f a0 Z = f(a0).
a0 " Z a0 " f(a0) (") a0 8" Z,
Z = f(a0). a 8" f(a0), (") a0 " Z,
Z = f(a0).
f,
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