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March 9th, 2018, 08:32 AM  #1 
Senior Member Joined: Mar 2015 From: New Jersey Posts: 1,301 Thanks: 94  Cantor's Diagonal Argument
Suppose I have a set of all infinite sequences of binary digits. Either I know the digits of each sequence or I don't. If I don't, how do I know they are all different? If I do, I can arrange them in numerical (countable) order. The list has a smallest member 0, and I can decide which of any two members is larger. Note by moderator: a numerical order doesn't trivially imply countability. Last edited by skipjack; March 9th, 2018 at 09:41 AM. 

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argument, cantor, diagonal 
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