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The actual contradiction proof that the reals have larger cardinality than the natural numbers uses the binary representation of decimals. See Cantor's diagonal
by stanleydrew 17y ago
The actual contradiction proof that the reals have larger cardinality than the natural numbers uses the binary representation of decimals. See Cantor's diagonal argument: http://en.wikipedia.org/wiki/Cantors_diagonal_argument http://en.wikipedia.org/wiki/Cantors_diagonal_argument.
- benmathes 17y agoIt doesn't require binary representation at all. You can write down all the numbers in any base and the argument still holds.
- stanleydrew 17y agoYes, clearly. I just find it interesting that in his original diagonal argument proof he chose the decimal representation.
- stanleydrew 17y agoEdit: binary not decimal.
- flatline 17y agoI always found the base-10 argument easier to see at a glance, and most people are probably more familiar with decimal notation. This guy writes to try and make math more popular, so I'd imagine that's his motivation. For Cantor, I would imagine that the formal proof was simpler to write out using the binary representation. Just a guess.