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This was asked by blogegog on a YouTube comment (gasp!):

[Regarding Cantor's diagonal argument:]

Couldn't I just make the same statement about rational numbers and say, 'take the largest number [sic he probably meant the one with the most digits] on the chart and append to the end of it a 1 if I'm hungry, or a 2 if I'm not' to show that his list of rational numbers doesn't contain them all?

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    I suggest you have a look at previous questions on this site - this has surely come up before.2012-08-09
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    "Largest on the chart", "the one with the most digits in the chart" are both nonsenses of the same caliber and mean nothing mathematically (I'm assuming that by *chart* you meant the *list* of numbers between zero and one usually used in the diagonal proof of Cantor's theorem) and, of course, "appending" stuff to "the end" of a number with a probably infinite decimal expansion is a nonsense two levels higher than the above ones.2012-08-09
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    possible duplicate of [Proof that the irrational numbers are uncountable](http://math.stackexchange.com/questions/732/proof-that-the-irrational-numbers-are-uncountable)2012-08-09
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    Related: A very thorough discussion of Cantor's diagonal argument was given by Arturo in an answer to *[How does Cantor's diagonal argument work?](http://math.stackexchange.com/q/39269/5363)*2012-08-09
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    There are also [Cardinality of the Irrationals](http://math.stackexchange.com/questions/72130/) and [Are there many more irrational numbers than rational?](http://math.stackexchange.com/questions/10333/).2012-08-09
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    Possible duplicate of [Produce an explicit bijection between rationals and naturals?](https://math.stackexchange.com/questions/7643/produce-an-explicit-bijection-between-rationals-and-naturals)2018-03-20

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