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March 9th, 2018, 08:32 AM   #1
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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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March 9th, 2018, 08:34 AM   #2
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