可数集可计算数判定性问题与图灵机
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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, 1/1 2/1 100000/1 1/1, 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、/2, 3/1, -3/1,1/3, -1/3, 有理数集是可数的 2 x2 - 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,
3、, 9x = 0,x2 = 0, 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
4、= 0, , 2x9 = 0,3x2 = 0, 3x3 = 0, , 3x9 = 0, 9x 2 = 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, 9x 2 = 0, 9x3 = 0, , 9x9 = 0,x10 = 0, x11 = 0, x12 = 0, , x99 = 0, x = 0,2x
5、= 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, 9x 2 = 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,-
6、x = 0,10 x = 0, 11x = 0, , 99x = 0,2x2 = 0, 2x3 = 0, , 2x9 = 0,3x2 = 0, 3x3 = 0, , 3x9 = 0, 9x 2 = 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,
7、 11x = 0, , 99x = 0,2x2 = 0, 2x3 = 0, , 2x9 = 0,3x2 = 0, 3x3 = 0, , 3x9 = 0, 9x 2 = 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, e 0.235711131719. 什么叫做“可以计
8、算的”？ x2 + y2 = z2 32 + 42 = 52 62 + 82 = 102 52 + 122 = 132 82 + 152 = 172 x3 + y3 = z3 x3 + y3 + 1 = z3 63 + 83 + 1 = 93 x3 + y3 - 1 = z3 93 + 103 - 1 = 123 x3 + y3 + z3 = w3 33 + 43 + 53 = 63 x4 + y4 + z4 = w4 26824404 + 153656394 + 187967604 = 206156734 x3 + y3 = z3 xn + yn = zn (n3) x2 - 2y2 = 0
9、 x2 = 2y2 x2 / y2 = 2 (x/y)2 = 2 xn + yn = zn (n3) x2 + 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 = 0.808080
10、8080.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. = a1 = 0.3141592653.a2 = 0.8080808080.a3 = 0.6700000000.a4 = 0.2222222222.a5
11、= 0.6180339887.a6 = 0.1249494949.a7 = 0.4758315839. = 0. a1 = 0.3141592653.a2 = 0.8080808080.a3 = 0.6700000000.a4 = 0.2222222222.a5 = 0.6180339887.a6 = 0.1249494949.a7 = 0.4758315839. = 0.4 a1 = 0.3141592653.a2 = 0.8080808080.a3 = 0.6700000000.a4 = 0.2222222222.a5 = 0.6180339887.a6 = 0.1249494949.a7
12、 = 0.4758315839. = 0.41 a1 = 0.3141592653.a2 = 0.8080808080.a3 = 0.6700000000.a4 = 0.2222222222.a5 = 0.6180339887.a6 = 0.1249494949.a7 = 0.4758315839. = 0.411 a1 = 0.3141592653.a2 = 0.8080808080.a3 = 0.6700000000.a4 = 0.2222222222.a5 = 0.6180339887.a6 = 0.1249494949.a7 = 0.4758315839. = 0.4113 a1 =
13、0.3141592653.a2 = 0.8080808080.a3 = 0.6700000000.a4 = 0.2222222222.a5 = 0.6180339887.a6 = 0.1249494949.a7 = 0.4758315839. = 0.41134 a1 = 0.3141592653.a2 = 0.8080808080.a3 = 0.6700000000.a4 = 0.2222222222.a5 = 0.6180339887.a6 = 0.1249494949.a7 = 0.4758315839. = 0.411340 a1 = 0.3141592653.a2 = 0.8080808080.a3 = 0.6700000000.a4 = 0.2222222222.a5 = 0.6180339887.a6 = 0.1249494949.a7 = 0.4758315839. = 0.4113406 a1 = 0.3141592653.a2 = 0.8080808080.a3 = 0.6700000000.a4 = 0.2222222222.a5 = 0.6180339887.a6 = 0.1249494949.a7 = 0.4758315839. = 0.4113406. 邱奇-图灵论题：图灵机是一种终极表达工具 谢谢大家顾森 (Matrix67)
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