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January 14th, 2015, 01:27 PM  #1 
Newbie Joined: Jan 2015 From: California Posts: 2 Thanks: 0  How to prove P(N) is uncountable ?
How do i prove that P(N) is uncountable, I can't use the diagonalization method for sure here. Can anyone explain how do I go about solving this ? One hint is that I have to equate P(N) to another uncountable set such as set of Real numbers. or a infinite number of sets which contain infinite sequence of binary. A = {0 ,1,1,0,0,0,1,....} B = {1,1,0,1,1,0,1......} C = {0,0,1,0,0,1,0,.....} ... ... How do I give relation between P(N) and the above given sets ? 
January 14th, 2015, 08:45 PM  #2  
Senior Member Joined: Jan 2012 From: Erewhon Posts: 245 Thanks: 112  Quote:
You will find such a proof here CB  
January 15th, 2015, 05:42 PM  #3  
Global Moderator Joined: May 2007 Posts: 6,528 Thanks: 589  Quote:
A is set containing 2,3,7,... B is set containing 1,2,4,5,7,... C is set containing 3,6,... Assuming you have a complete countable list, then you can construct a set not in the list by the usual method.  
January 19th, 2015, 10:02 PM  #4 
Newbie Joined: Jan 2015 From: California Posts: 2 Thanks: 0 
Thank you 

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