若集[tex=0.786x1.0]Yn3GgEZev6SOu2r4v1WnCw==[/tex]中每个元素，由互相独立的可数个指标一对一决定，即[tex=5.786x1.357]2Yrj2BM7ZaU5mqvRI1wU8Kj1b09VOTdpcd6MJ58ggtQ5QeP/fOb7OMQuteK5i6D/[/tex]，而每个[tex=0.857x1.0]l7ziQUB2lQg4WPE3STkrFw==[/tex]取遍一个基数为[tex=0.5x0.786]EL0hSqs6jZBGdsmH7TMShQ==[/tex]的集，则[tex=0.786x1.0]Yn3GgEZev6SOu2r4v1WnCw==[/tex]的基数也是[tex=0.5x0.786]EL0hSqs6jZBGdsmH7TMShQ==[/tex]

2022-06-01

若集[tex=0.786x1.0]Yn3GgEZev6SOu2r4v1WnCw==[/tex]中每个元素，由互相独立的可数个指标一对一决定，即[tex=5.786x1.357]2Yrj2BM7ZaU5mqvRI1wU8Kj1b09VOTdpcd6MJ58ggtQ5QeP/fOb7OMQuteK5i6D/[/tex]，而每个[tex=0.857x1.0]l7ziQUB2lQg4WPE3STkrFw==[/tex]取遍一个基数为[tex=0.5x0.786]EL0hSqs6jZBGdsmH7TMShQ==[/tex]的集，则[tex=0.786x1.0]Yn3GgEZev6SOu2r4v1WnCw==[/tex]的基数也是[tex=0.5x0.786]EL0hSqs6jZBGdsmH7TMShQ==[/tex]

答案：

设[tex=10.0x1.643]3G1wSAwGKFRMe0pdlD+C5yDPh41MGvGbTixkO1+0yLwCIyXKWR5mCR9JwZ9I4U7bBuUGRhm2SsJDzRse9S9sFw==[/tex]因而有[tex=1.0x1.214]134fDfyZx2aGiyeQW3vIfw==[/tex]到实数集[tex=0.786x1.0]as0RCzgUx1oS48cKHRAVVg==[/tex]的一一映射[tex=0.929x1.0]KqmjpHP/yC2M8a3THmhv5w==[/tex].令[tex=0.714x1.0]OqF+/h/mAb1/2XhJuj27xg==[/tex]是[tex=0.786x1.0]Yn3GgEZev6SOu2r4v1WnCw==[/tex]到[tex=1.5x1.214]YVFonG54kD0IofCG8cFnxw==[/tex]的一映射，对任意[tex=23.143x1.357]5kKWlLVFjxRHMt9OICtsn7N+CVcVkYBGSCXwgO/QvXFSELZNm9/2LYDTXYI1iF/ihOsNq3q3LHP2FiRfaowLbVO34jMAhthMT+7wbUMsrUYj1HLmht8JdnzfS6wHi2k7gf1v68erZgmajIiDka3NV8IUWORpAbcwt+eUkDClZEAhSq3cPoxbXoAxm6NyE9MtWDrhOUkjFGs9XSLBh9dCM/ygyuJFhdSQhpsMItpYM0WYu5WBroYitPorrvvT69e+arMLyJNIapJZEd3LDeQegg==[/tex].下面证明[tex=0.714x1.0]OqF+/h/mAb1/2XhJuj27xg==[/tex]是一一映射.若[tex=10.214x1.571]qCxzSW7+9SGttcQl5GWd9R55F1NEnlIDieIVGBpc1asepIDxcMY/yMGQOVkNai2dDi97RYCZdOIO4SqynRAdNcnkyfJMCFgZtyWRfIacVfVK3xRQFBro0qTLg8DgZ7RO0CGLYIyY46SYmbi4SPuKtjMuQSZqmYB5urNbn1y3BS8=[/tex]，则对任意[tex=7.071x1.429]z+e7B5BZqR1DVtawYI5xzdc6XlV6bnSS3lvf0oP8DzYAm86BJtIZKpkRevDc1Ttm1v2pKV0y7fJNqM/XX9x4uhoGTEXKnzfse7FU/ziNRD8=[/tex].由于[tex=0.929x1.0]3iHmioLfVzl6otL5pNY6Hw==[/tex]是一对一的，因此[tex=2.429x1.429]oa0rh9vAWai+JBasSXH428lLW0exaTPJENf1i8LBGvs=[/tex]所以[tex=6.929x1.214]5kKWlLVFjxRHMt9OICtsn3/m6V/gKWVhd6ZKX+u1/3fy/PlIXoh825Z+ADfO4CQoQsTrW42hq0FjjVBW3jJC/ZwwndsfKLc6niWHajj/6CTyhjzeHG3gNz7axFdQYRgj[/tex]对任意[tex=15.929x1.357]TASgeax8JPipKY1zvB3ZBsa/aAvZeholj198e9MvXUHGxKf1kgqY9d5kypJkZmE7xypjd3ONVOldeO1g0Fk7NUZJLYQI0hQZwseAbIxfZ03W+uDX0kml5g7Vmdo7dkEQ[/tex]，因为[tex=0.929x1.0]3iHmioLfVzl6otL5pNY6Hw==[/tex]是映上的，必有[tex=2.5x1.214]3G1wSAwGKFRMe0pdlD+C5ybfPaXevmg9VkJfXQRlrdQ=[/tex]，使[tex=4.571x1.357]YFa+L91nQKZvaVn7fXkxnGzZ8qocqGqKKuz3MwuCcvYNieYpqweE9DDcZsBXuQcb[/tex]所以有[tex=4.5x1.286]5kKWlLVFjxRHMt9OICtsnxlbQhzbueClNQkxeZ2GAK6CnqbsmwlKquFroh9CZfQW[/tex]，使[tex=20.214x1.357]qCxzSW7+9SGttcQl5GWd9Q1RnNJLkGMjyH43bRQBWJpb45hau6Xl07y0HyRX9DHFpFzLmYoKzB5j1xLM99CZ316UhfgwnX2fdWotaOBiHqrwydzOx37JHGCyQw4IpAstnYJZ0fVyagtvSG+CaOlE2SrANC+lzqMe1hROHrI2mQgbhICceLHP0+5z4X5xSTFL7EOjH197pZMjBPoKuYsH3XFF5XzEDAAVDbdY6Oh7MVo=[/tex]，即[tex=0.714x1.0]OqF+/h/mAb1/2XhJuj27xg==[/tex]是一一映射. 所以[tex=0.786x1.0]Yn3GgEZev6SOu2r4v1WnCw==[/tex]与[tex=1.5x1.214]YVFonG54kD0IofCG8cFnxw==[/tex]的基数相同，等于[tex=0.5x0.786]EL0hSqs6jZBGdsmH7TMShQ==[/tex]

举一反三

内容

0
对 [tex=0.643x0.786]/he/ol8BkDuTTL9yMPtH4Q==[/tex]的不同值，分别求出循环群[tex=1.143x1.214]StMMJ6qThnpokZJIPGrdFyP3vrLnUdltYxmLxjw8za8=[/tex]的所有生成元和所有子群。(1) 7; (2) 8; (3)10 ;(4) 14 ; (5) 15 (6) 18 。
1
>>>x= [10, 6, 0, 1, 7, 4, 3, 2, 8, 5, 9]>>>print(x.sort()) 语句运行结果正确的是( )。 A: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10] B: [10, 6, 0, 1, 7, 4, 3, 2, 8, 5, 9] C: [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0] D: ['2', '4', '0', '6', '10', '7', '8', '3', '9', '1', '5']
2
对素数 [tex=0.571x1.0]FGGpnaR8m8C48rN8O0c7aw==[/tex] 的不同值, 找出循环群[tex=1.143x1.357]oOz0oH4UpFaaOY7OuGotcg8wtMntQEjCiVorwD1W3R4=[/tex]的所有生成元和所有子群.(1) 7 ; (2) 11 ; (3) 13(4) 17 ; (5) 19 ; (6) 23 .
3
判断下列命题是否为真：（1）[tex=3.643x1.357]/5abqJjwKZ1qr+6hsVFF5EBvfq3ggOFNlHMClz0h9nk=[/tex]（2）[tex=2.929x1.357]rGJpyjIjJpbcoBTWxP0Jiw==[/tex]（3）[tex=4.5x1.357]2wycHMoqU83MyEp17iBils58bR7YLuCTI2G9NVAdlfY=[/tex]（4）[tex=5.214x1.357]CTz2gu+IIm1GgNmYMGaduCRtA41wnW4WqwRWwEhq6aA=[/tex]（5）[tex=4.857x1.357]1DcE2BMMOaZhTuxR/mjgsboXxfg5ET59Dp4I/jjEDuw=[/tex]（6）[tex=4.643x1.357]BSryrsQYOvTP2hTWRu6t4nAuJwlSs4L9jaq70EpB+Us=[/tex]（7）若[tex=6.0x1.357]y0IZLUnBO88nR8WBZYvd7QXv5S1OMINV5cQNzPyiyAc=[/tex]，则[tex=3.429x1.357]1brfPwTkVVIX4GfoMIUskA==[/tex]（8）若[tex=7.643x1.357]MhLfJXZnhbXiB0x3oNtFzThV4Y1mJxe1VYr7PkJE/T6hmTD3WWp+UxbNwvUQ6DHk[/tex]，则[tex=4.143x1.357]LZUA94ISo1po5HWsOVeBCjo0rMvj7uw3bGw5HiZenrI=[/tex]
4
上颌恒牙萌出的顺序为：（） A: 6 1 2 4 5 3 7 8 B: 1 2 4 3 5 6 7 8 C: 6 1 2 4 3 5 7 8 D: 6 1 2 3 4 5 7 8 E: 1 6 2 4 3 5 7 8