<P>장재영 선생님의 답글입니다.</P> <P> </P> <DIV class=board> <P>(3)Let S be the set of all sequences of 0's and 1's. </P> <P>For example, 1010101..., 01111111..., and 010110111... are in S.</P> <P>Prove that S is uncountable.</P> <P>pf) For <OBJECT class=MATH classid=clsid:70E4BF88-2729-4A46-8794-D459BAC0EB63 width=54 align=absMiddle height=26><PARAM NAME="_cx" VALUE="1428"><PARAM NAME="_cy" VALUE="687"><PARAM NAME="BackColor" VALUE="3932222"><PARAM NAME="Enabled" VALUE="-1"><PARAM NAME="Script" VALUE="[0]#wh4/12.6`5.6/12,[1]{{forall}^^{s}`in` S}/{#xc333333}"><PARAM NAME="FontSize" VALUE="12"><PARAM NAME="FontColor" VALUE="3355443"><PARAM NAME="Editable" VALUE="0"><PARAM NAME="Measurable" VALUE="0"></OBJECT>, </P> <P>correspond the subset of N(=the set of all natural numbers) such that {n <OBJECT class=MATH classid=clsid:70E4BF88-2729-4A46-8794-D459BAC0EB63 width=17 align=absMiddle height=18><PARAM NAME="_cx" VALUE="449"><PARAM NAME="_cy" VALUE="476"><PARAM NAME="BackColor" VALUE="3932222"><PARAM NAME="Enabled" VALUE="-1"><PARAM NAME="Script" VALUE="[0]#wh4/4`4.3/12,[1]{in}/{#xc333333}"><PARAM NAME="FontSize" VALUE="12"><PARAM NAME="FontColor" VALUE="3355443"><PARAM NAME="Editable" VALUE="0"><PARAM NAME="Measurable" VALUE="0"></OBJECT>N : n th coordinate of s is 1}.</P> <P>Then this projection is a bijection from S to the power set of N.</P> <P>Therefofe S is uncontable. - q. e. d</P></DIV>
