. , . . , , , , .
.1. | , . |
1. 2. 3. 4. 5. , |
. , (), 15 .
15. 1 , 1. 2 .
|
, 1
→ x → s(x) →
|
4 , (2) . 3 ,
|
, 5 , 14
|
(18581932), (3). .
.2. | |
, 15, (3) N | |
1. 1 $ x (x:= 1) | |
2. x S(x), x "x $ y (y = S(x)) "x, y (y = x Þ S(x) = S(y)) | |
3. "x (S(x) ¹ 1) | |
4. "x, y (S(x) = S(y) Þ x=y) | |
5. . ΜÌΝ 1, x 24 ( 14 T(x)). Ν Ì Μ | |
"x (xÎM)L(T(x)) Þ M=N |
|
|
, , , . , (18871963). (3)
→ a2 → α1 → α0 → α1 → a2 →
, S. y
y = S (S (S(1))),
S (S (S(1))) - .
y .
,
1, 2, 3, , n, n +1, , , . 0, 1, 2, , 9. , , " a Î N
a = a n a n 1 a1a0 = a n˙ 10 n + a n 1 ˙ 10 n 1 + + a1 ˙ 10 + a0,
a0, a1, , anÎ(0, 1, , 9)Ù(a n ¹0).
.2, , . , , . .
1.2. ,
. . :
N | L | +; " " | Z (, ) | |
Z | L | ; : . | Q |
2
1
m/n, : m, n, N, n 0 Q. , ´,:, .
, , .
, , .
: a N
a = anKn +... + a 1 K + a o(5)
. a o, a 1 ,..., a n 0,1,2,..., K1. K 10, K 0,1,2,..., 1. () 1, 2 ,..., n ( , , ).
|
|
K , , .
.
.
= 247 = 2 . 102 +4 . 10+7, = 378 = 3 . 102 + 7 . 10 + 8
= +.
, , , :
7+8 = 10+5 ()
4.10 + 7 . 10 = 102+10 ()
2 . 102 + 3 . 102 = 5 . 102 ()
, = +:
= (102 +5 . 102) + (10+10)+5 = 6. 102 +2 . 10+5 = 625
.
, 197<211, 197<2.102, 211 > 2.102.
, .
, (6)
:
(7)
, (6) (7) .
a, b N, (a > b) m, n N, (m<a, n<b) ,
= bm+n (8)
2
, , , .
1
(7) , , .. , :
(9)
, ,
, (9) n :