可数集、可计算数、判定性问题与图灵机

1、可数集、可计算数、判定性问题与图灵机顾森 (Matrix67)枚举所有可能的数1, 2, 3, 4, 5, 6, 0, 1, -1, 2, -2, 3, -3, 1/2, 1/3, 1/4, 1/5, 1/2, 1/3, 2/3, 1/4, 3/4, 1/5, 2/5, 3/5, 4/5, 1/6,5/6, 1/7, 2/7, 1/2, 3/2, 5/2, 7/2, 1/12/1100000/11/1, 2/1, 1/2, 3/1, 1/3, 4/1, 3/2, 2/3, 1/4, 5/1,1/5, 6/1, 5/2, 0, 1/1, -1/1, 2/1, -2/1, 1/2, -1/2, 3

2、/1, -3/1,1/3, -1/3, 有理数集是可数的2x2 - 2 = 0 x5 + 2x4 - 3x - 6 = 0- 2, 43 , - 43 x5 - x - 1 = 0 x = 1.1673.代数数集是可数的吗？x = 0,x + 1 = 0,x + 2 = 0,x + 3 = 0,999x + 9999 = 0- 999x - 9999 = 0 x - 1 = 0,x2 - 1 = 0,x3 - 1 = 0,x4 - 1 = 0,x = 0,x = 0,2x = 0, 3x = 0, , 9x = 0,x = 0,2x = 0, 3x = 0, , 9x = 0,x2 = 0,

3、x3 = 0, , x9 = 0,x = 0,2x = 0, 3x = 0, , 9x = 0,x2 = 0, x3 = 0, , x9 = 0,- x = 0,x = 0,2x = 0, 3x = 0, , 9x = 0,x2 = 0, x3 = 0, , x9 = 0,- x = 0,10 x = 0, 11x = 0, , 99x = 0,x = 0,2x = 0, 3x = 0, , 9x = 0,x2 = 0, x3 = 0, , x9 = 0,- x = 0,10 x = 0, 11x = 0, , 99x = 0,2x2 = 0, 2x3 = 0, , 2x9 = 0,3x2 =

4、 0, 3x3 = 0, , 3x9 = 0, 9x2 = 0, 9x3 = 0, , 9x9 = 0,x = 0,2x = 0, 3x = 0, , 9x = 0,x2 = 0, x3 = 0, , x9 = 0,- x = 0,10 x = 0, 11x = 0, , 99x = 0,2x2 = 0, 2x3 = 0, , 2x9 = 0,3x2 = 0, 3x3 = 0, , 3x9 = 0, 9x2 = 0, 9x3 = 0, , 9x9 = 0,x10 = 0, x11 = 0, x12 = 0, , x99 = 0,x = 0,2x = 0, 3x = 0, , 9x = 0,x2

5、 = 0, x3 = 0, , x9 = 0,- x = 0,10 x = 0, 11x = 0, , 99x = 0,2x2 = 0, 2x3 = 0, , 2x9 = 0,3x2 = 0, 3x3 = 0, , 3x9 = 0, 9x2 = 0, 9x3 = 0, , 9x9 = 0,x10 = 0, x11 = 0, x12 = 0, , x99 = 0,x + 1 = 0, x + 2 = 0, , x + 9 = 0,x = 0,2x = 0, 3x = 0, , 9x = 0,x2 = 0, x3 = 0, , x9 = 0,- x = 0,10 x = 0, 11x = 0, ,

6、 99x = 0,2x2 = 0, 2x3 = 0, , 2x9 = 0,3x2 = 0, 3x3 = 0, , 3x9 = 0, 9x2 = 0, 9x3 = 0, , 9x9 = 0,x10 = 0, x11 = 0, x12 = 0, , x99 = 0,x + 1 = 0, x + 2 = 0, , x + 9 = 0,x - 1 = 0, x - 2 = 0, , x - 9 = 0,x = 0,2x = 0, 3x = 0, , 9x = 0,x2 = 0, x3 = 0, , x9 = 0,- x = 0,10 x = 0, 11x = 0, , 99x = 0,2x2 = 0,

7、 2x3 = 0, , 2x9 = 0,3x2 = 0, 3x3 = 0, , 3x9 = 0, 9x2 = 0, 9x3 = 0, , 9x9 = 0,x10 = 0, x11 = 0, x12 = 0, , x99 = 0,x + 1 = 0, x + 2 = 0, , x + 9 = 0,x - 1 = 0, x - 2 = 0, , x - 9 = 0,- 2x = 0, - 3x = 0, , - 9x = 0,- x2 = 0, - x3 = 0, , - x9 = 0,e0.235711131719.什么叫做“可以计算的”？x2 + y2 = z232 + 42 = 5262 +

8、 82 = 10252 + 122 = 13282 + 152 = 172x3 + y3 = z3x3 + y3 + 1 = z363 + 83 + 1 = 93x3 + y3 - 1 = z393 + 103 - 1 = 123x3 + y3 + z3 = w333 + 43 + 53 = 63x4 + y4 + z4 = w426824404 + 153656394 + 187967604 = 206156734x3 + y3 = z3xn + yn = zn (n3)x2 - 2y2 = 0 x2 = 2y2x2 / y2 = 2(x/y)2 = 2xn + yn = zn (n3)x2

9、 + y2 = a2x2 + z2 = b2y2 + z2 = c2x2 + y2 + z2 = d2希尔伯特：通用判定法？有什么东西是不可数的吗？康托尔：实数是不可数的a1 = 0.3141592653.a2 = 0.8080808080.a3 = 0.6700000000.a4 = 0.2222222222.a5 = 0.6180339887.a6 = 0.1249494949.a7 = 0.4758315839. a1 = 0.3141592653.a2 = 0.8080808080.a3 = 0.6700000000.a4 = 0.2222222222.a5 = 0.618033988

10、7.a6 = 0.1249494949.a7 = 0.4758315839. a1 = 0.3141592653.a2 = 0.8080808080.a3 = 0.6700000000.a4 = 0.2222222222.a5 = 0.6180339887.a6 = 0.1249494949.a7 = 0.4758315839. =a1 = 0.3141592653.a2 = 0.8080808080.a3 = 0.6700000000.a4 = 0.2222222222.a5 = 0.6180339887.a6 = 0.1249494949.a7 = 0.4758315839. = 0.a1

11、 = 0.3141592653.a2 = 0.8080808080.a3 = 0.6700000000.a4 = 0.2222222222.a5 = 0.6180339887.a6 = 0.1249494949.a7 = 0.4758315839. = 0.4a1 = 0.3141592653.a2 = 0.8080808080.a3 = 0.6700000000.a4 = 0.2222222222.a5 = 0.6180339887.a6 = 0.1249494949.a7 = 0.4758315839. = 0.41a1 = 0.3141592653.a2 = 0.8080808080.a

12、3 = 0.6700000000.a4 = 0.2222222222.a5 = 0.6180339887.a6 = 0.1249494949.a7 = 0.4758315839. = 0.411a1 = 0.3141592653.a2 = 0.8080808080.a3 = 0.6700000000.a4 = 0.2222222222.a5 = 0.6180339887.a6 = 0.1249494949.a7 = 0.4758315839. = 0.4113a1 = 0.3141592653.a2 = 0.8080808080.a3 = 0.6700000000.a4 = 0.2222222

13、222.a5 = 0.6180339887.a6 = 0.1249494949.a7 = 0.4758315839. = 0.41134a1 = 0.3141592653.a2 = 0.8080808080.a3 = 0.6700000000.a4 = 0.2222222222.a5 = 0.6180339887.a6 = 0.1249494949.a7 = 0.4758315839. = 0.411340a1 = 0.3141592653.a2 = 0.8080808080.a3 = 0.6700000000.a4 = 0.2222222222.a5 = 0.6180339887.a6 = 0.1249494949.a