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N=hlog 9/0.9ε
log 1/0.1i=hlog(10/ε)
log 10 i=h1 + log 1/ε
log 10 i= 1 + hlog 1/ε
log 10 i
1
10 n+1 <¯
¯
¯0,
n
z }| {
999 ···9−1¯
¯
¯=1
10 n<1
10 (n−1) (N5n)
0,
n
z }| {
999 ···9 1
0,z }| {
999 ···
0,z }| {
999 ··· = 1
43
30 = 1 + 13
30 = 1 + 1
30
13
= 1 + 1
2 + 4
13
= 1 + 1
2 + 1
3 + 1
4
43
30 ≡1 + 1
2
1
3
1
4
++
43
30 ≡(1; 2,3,4)
r
r≡r(n) = (k(0) ;k(1) , k(2) ,··· , k(n−1) , k(n))k(0)
k(1), k (2) ,··· , k (n−1), k(n)
n ω
n
ω≡ω(n) = (k(0);k(1), k(2),··· , k (n−1), ξ (n))ξ(n)
ω
ω= (k(0);k(1), k(2),··· , k (n−1), k(n),···)
1)
√2 = 1 + 1
2
1
2= (1; 2 ,2,2···) = (1; ˙
2)
+ + ···