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Apr 14, 2010 at 3:55 comment added user4977 Also related, it is difficult to give an example of a continuous real valued function on [0,1] that is not monotone on any interval, but it is not too difficult to prove using the Baire category theorem that almost all functions are like this.
Apr 13, 2010 at 18:13 comment added Qiaochu Yuan A related example: it's not completely trivial to write down a language that can't be recognized by a Turing machine, but there are uncountably many languages and countably many Turing machines.
Apr 13, 2010 at 17:07 history edited Ryan Thorngren CC BY-SA 2.5
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Apr 13, 2010 at 17:01 history answered Ryan Thorngren CC BY-SA 2.5