A Conversation for What I don't like about Cantor’s Diagonal Argument
Cantor's Diagonalization Argument.
john_gabriel Started conversation Jan 19, 2008
This argument is nonsense and anyone believing it is capable of believing anything. Visit http://mathphile.blogspot.com/ to see how the real numbers are infinitely 'countable' according to Cantor's definition.
Cantor's Diagonalization Argument.
aging jb Posted Jan 19, 2008
Well now, let us suppose that the reals between 0 and 1 are countable, and see what that implies.
Countability implies that each real can be placed in correspondence to an integer - a list. Now take each real in turn and construct an interval including the real. Make the first interval of length 1/5, the next of length 1/25, and so on. This sequence of intervals clearly covers all the reals, if they are countable, but its total length is only 1/4. Three quarters of the interval between 0 and 1 is missing...
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Cantor's Diagonalization Argument.
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