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 Post subject: UncountablePosted: Thu, 22 Sep 2011 02:45:53 UTC
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Joined: Tue, 6 Sep 2011 04:11:20 UTC
Posts: 19
I'm going to assume this is similar to Cantor's diagonal proof, but I'm having trouble "seeing" the exact correlation.

Let A={b | b is a sequence of 0's and 1's} Prove a is uncountable.

Let X be a countable subset of A. Let xn represent all sequences with n elements. Then X can be written as

Xn = {bn,m} where m is the mth element of xn}

So,
x1={b1,1}
x2={b2,1 , b2,2}
xn={bn,1 , bn,2 , ... , bn,m}

I think I'm making a mess of it. Any guidance would be appreciated.

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 Post subject: Re: UncountablePosted: Thu, 22 Sep 2011 04:06:38 UTC
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Joined: Mon, 23 Feb 2009 23:20:33 UTC
Posts: 1049
If all the binary sequences in the set are of finite length, the statement is false. So the intention must be that the set contains all binary sequences of infinite length. But this is just a matter of regurgitating Cantor's diagonal argument without alteration.

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