设[tex=1.429x1.071]F3TBtXtxusVWuZn0YSmGXg==[/tex][tex=1.143x1.214]99izTVkOg6z3Ylatn6B9Ww==[/tex]是非空有界完备集合.证明：存在[tex=1.143x1.214]99izTVkOg6z3Ylatn6B9Ww==[/tex]上连续函数[tex=0.5x1.214]++gGGJQcubEKWlse37f6tQ==[/tex]满足：[tex=8.5x1.5]WuvHoUh4KPLyfxzlr24+GfSGDWLefbuFDdJ/f331ZXXkFNGMMpoGppdOybekb/9L2EtOduG6qbqU+5+shcPXUs2M++6pz14Ok9xvE6SqP0o=[/tex](1)[tex=9.571x1.357]fxfviK1YBkYmgn9XgOYAcfaCNQUbI+BtwvoEA3LWIS6QAcqVSlwm/KByOLusQmtzeyINKIxsRLrJSN+78SAnCG8tT71vz4ZmtcmipB2dIO0zSMwbC35Y8mqkIkdcTiN0[/tex](2)[tex=7.929x1.357]SpAMdDaLShh1ZQW1TY7em+AzIUbyCn8mPJ5QyJwBAx0=[/tex](3)

2022-06-29

设[tex=1.429x1.071]F3TBtXtxusVWuZn0YSmGXg==[/tex][tex=1.143x1.214]99izTVkOg6z3Ylatn6B9Ww==[/tex]是非空有界完备集合.证明：存在[tex=1.143x1.214]99izTVkOg6z3Ylatn6B9Ww==[/tex]上连续函数[tex=0.5x1.214]++gGGJQcubEKWlse37f6tQ==[/tex]满足：[tex=8.5x1.5]WuvHoUh4KPLyfxzlr24+GfSGDWLefbuFDdJ/f331ZXXkFNGMMpoGppdOybekb/9L2EtOduG6qbqU+5+shcPXUs2M++6pz14Ok9xvE6SqP0o=[/tex](1)[tex=9.571x1.357]fxfviK1YBkYmgn9XgOYAcfaCNQUbI+BtwvoEA3LWIS6QAcqVSlwm/KByOLusQmtzeyINKIxsRLrJSN+78SAnCG8tT71vz4ZmtcmipB2dIO0zSMwbC35Y8mqkIkdcTiN0[/tex](2)[tex=7.929x1.357]SpAMdDaLShh1ZQW1TY7em+AzIUbyCn8mPJ5QyJwBAx0=[/tex](3)

答案：

证明.设[tex=1.429x1.071]F3TBtXtxusVWuZn0YSmGXg==[/tex][tex=1.143x1.214]99izTVkOg6z3Ylatn6B9Ww==[/tex]是非空有界完备集合.若有闭区间[tex=3.429x1.357]p0JxOxVYJHf/vI9/I2wKJpmTBvkmF3L2Qhbrc9JBXf0=[/tex]，则定义[tex=1.643x1.357]N99frpoR4hhkgLzrp2Q6tQ==[/tex]为[tex=10.929x5.357]ZECRU93qHJI3rUoGf+vkZ2hvQ/BP1Bpomt/Wsif89X9afGhLpU1C6wul/v3S/9tZfTwG2HwtZi+m92UU7Mf+RLicmPXOW5CyoqcfjWPAtBw3ACzbfCIP6PT4Y5TAaFTm/QIQk4VZ1S7RYTTZahI3Uw==[/tex]则上述[tex=1.643x1.357]N99frpoR4hhkgLzrp2Q6tQ==[/tex]满足三个条件且连续.设不存在闭区间[tex=3.429x1.357]p0JxOxVYJHf/vI9/I2wKJpmTBvkmF3L2Qhbrc9JBXf0=[/tex].由本节定理[tex=0.5x1.0]W06Tg26W3mNchdIehLD5rg==[/tex]，考虑[tex=6.714x3.286]WjVyuT42ihOrat8Vk7jE/YfphxmOhLr75ERPZAAZj3KGvqU2jQ2e1Gw1yrzx2tgJ[/tex]其中[tex=1.071x1.214]KWMsZjnmxkcJvQUEkK1CFA==[/tex]为彼此没有公共端点的不交开区间，且与闭区间无公共端点.将其排成序列[tex=9.214x1.357]XZ77iEbnFxrm8rflebBgZv8HJ+n0bCWIoKHRzc3Bzu5Jlnlbyvtlf7sfdVTI1oi6ELvOl/zG4/UDyIM5Wcy2DQ==[/tex].记[tex=4.643x1.357]nLjcEnlnTvUnUmVDFUQwb6B6Kb4PtjzLI7n6edVJOQxLfZm4D7sBgtv2Q4sTZKQo[/tex][tex=2.5x1.071]7LdKmkSlODqVFlKBvNmN9LeZwBAE29wNm0PE1lji1ic=[/tex].定义[tex=15.643x1.357]2vx0byAKaehWtJQCxYLc5cxourzxbPwL/WMWTp3gWI9wLYIZXQ547NTMCSt+3usx/nTh3pEy8bPSoT7iQX6hwqLo1Y3/6qeJt6uLtOKtBUz8f195D2mrp2ONm68TefkX[/tex].其中若[tex=2.786x1.071]qRFGqQkygWLFvIOHuja2ug==[/tex]，记[tex=2.143x1.214]hQ8y6ngrENATJwqwrD5dyg==[/tex].若[tex=2.714x1.214]7tFrM2VWSZ+HsItaC+tCAA==[/tex]，记[tex=2.143x1.214]8LPYCYCqY1Zan7mZgY1GYg==[/tex].又若[tex=2.786x1.071]qRFGqQkygWLFvIOHuja2ug==[/tex]，令[tex=8.143x1.357]1k28quGXYGoFEVqiz8BroUp6qwFl7inu8YX9hiSS6y/Y6q8QdyAEhvPOMFXE7v6f[/tex]，则若[tex=2.929x1.143]n9NX9s+yl/T5XFTXW8YBlAaDkQj1+3enG1APltabaX8=[/tex]，记[tex=2.143x1.214]9MiQs630Ql0JjO/+iOO9qA==[/tex].若[tex=2.857x1.286]HtmVNhAJVCsKUzPqLUmGZTzd+7d7MYpZhGqUWTd7ljo=[/tex]，记[tex=2.143x1.214]A+/jTyOJ2CUDpBuzC+QUeQ==[/tex].若[tex=2.714x1.214]WOq+k2DM4L3dFxZ7l0dY5A==[/tex]，令[tex=8.143x1.357]1k28quGXYGoFEVqiz8BroXOk/WGybtcADSj6Gq5kH7iefcjaSAvc1sc4Ru6p+VvU[/tex]，则若[tex=2.929x1.143]n9NX9s+yl/T5XFTXW8YBlAaDkQj1+3enG1APltabaX8=[/tex]记[tex=2.143x1.214]9MiQs630Ql0JjO/+iOO9qA==[/tex].若[tex=2.857x1.286]HtmVNhAJVCsKUzPqLUmGZTzd+7d7MYpZhGqUWTd7ljo=[/tex]，记[tex=2.143x1.214]A+/jTyOJ2CUDpBuzC+QUeQ==[/tex]这样进行下去，由于[tex=0.643x1.0]+oHlSEIghohvxH3XmTRlFg==[/tex]中没有闭区间，于是对于[tex=0.571x0.786]ZSLOI4fiO1oAbVC5M8IVkA==[/tex]，有唯一的[tex=1.857x1.357]SecLa13o9OepOeb/18XrrA==[/tex]与之对应.考虑[tex=2.786x1.357]mbdruYTLTb+9J7BTIk7rRDcUww67qNanwgVRd9QxfMM=[/tex][tex=6.357x1.214]brOFXtKdHrXbVmpg3AdwtdOPf6kk0AVewFEbIbrDBoneDYFYuBIyDVkYgXvRnmqg[/tex]其中[tex=6.357x1.214]brOFXtKdHrXbVmpg3AdwtdOPf6kk0AVewFEbIbrDBonFjTg2eMliDGYKmRBusgHT[/tex]为[tex=2.0x1.357]khGQOVqy3eZik4Tp7/+YjA==[/tex]上数的二进制表示，则其为单调增函数.又设[tex=12.214x3.929]hnh6U0l6JuDutlGflYm8m721e+AJnAu1Q8RH/wcDM5VR4foCkV6i3CCESJaMkqWwJ41BiwLb4iYwc/CPzKncRH1rGIsPJEYbYdgEAHgwvkAabTaOGaWeJ94QrFPWd3FxXxpBIrnq16TC/QOm2zaVJ2PxXZmYO+y2kJ1ydFzZYEY=[/tex]于是[tex=2.071x1.357]P1hDjpmiXlvx7XENIfKMDQ==[/tex]单调递增，且[tex=6.286x1.357]Kl9B8SSKSnBVFfUNf0/IZCrRDIRKvihb5I/Z0hdM02w=[/tex].由数学分析结论知[tex=2.071x1.357]P1hDjpmiXlvx7XENIfKMDQ==[/tex]连续.易证其为满足条件的函数.

举一反三

内容

0
‏ ‎‏设二维随机变量(X,Y)的联合分布列为‎‏ X‎‏Y‎ -1 0 1‎ -1‎ 1‎ 1/6 1/9 2/9‎ 1/3 0 1/6‎‏则P{XY=1}为( )‎‏‎ A: 0 B: 1/6 C: 1/3 D: 2/3
1
6个顶点11条边的所有非同构的连通的简单非平面图有[tex=2.143x2.429]iP+B62/T05A6ZTM0eeaWiQ==[/tex]个，其中有[tex=2.143x2.429]ndZSw3zT0QTOVLVdoUto1Q==[/tex]个含子图[tex=1.786x1.286]J+vVZa2YaMpc6mJBbqVvWw==[/tex]，有[tex=2.143x2.429]lmhx48evnQMhi03NovPXig==[/tex]个含与[tex=1.214x1.214]kFXZ1uR8GjycbJx+Ts2kyQ==[/tex]同胚的子图。供选择的答案[tex=3.071x1.214]3KinXFh3SXhZ7nIe1y9KEV6aadxhhJWeEy6Dij1iObdMUZkY6ZA5J2dVVjPSuhEf[/tex]：(1) 1 ;(2) 2 ;(3) 3 ; (4) 4 ;(5) 5 ;(6) 6 ; (7) 7 ; (8) 8 。
2
设DES加密算法中的一个S盒为： 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0 1 2 3 14 4 13 1 2 15 11 8 3 10 6 12 5 9 0 7 0 15 7 4 14 2 13 1 10 6 12 11 9 5 3 8 4 1 14 8 13 6 2 11 15 12 9 7 3 10 5 0 15 12 8 2 4 9 1 7 5 11 A: 1010 B: 0001 C: 1011 D: 0111
3
假设“☆”是一种新的运算，若3☆2=3×4，6☆3=6×7×8，x☆4=840(x＞0)，那么x等于： A: 2 B: 3 C: 4 D: 5 E: 6 F: 7 G: 8 H: 9
4
【单选题】myarray1=np.arange(15) myarray2=myarray1.reshape(5,3) print( myarray1) print(myarray2) 输出值是? A. [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15] [[ 0 1 2] [ 3 4 5] [ 6 7 8] [ 9 10 11] [12 13 14]] B. [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15] [[ 1 2 3] [ 4 5 6] [ 7 8 9] [10 11 12] [13 14 15]] C. [ 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14] [[ 0 1 2] [ 3 4 5] [ 6 7 8] [ 9 10 11] [12 13 14]] D. [ 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14] [[ 1 2 3] [ 4 5 6] [ 7 8 9] [10 11 12] [13 14 15]]