Timeline for Prove that a set is not countable

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Apr 22, 2014 at 18:19	comment	added	Mario Carneiro		@Harry The reason this is called the "diagonal technique" is because of the $f(n)(n)$ part. That is, we construct a function by drawing all the $0$'s and $1$'s of each function in a big matrix, then drawing a diagonal line on that matrix and make a new function from those terms (but flipped, so we get a contradiction).
Apr 22, 2014 at 18:15	comment	added	Mario Carneiro		@Harry A countable sequence is a function from the natural numbers (or a subset) to, in this case, $\{0,1\}$. For example, the sequence $\langle 1,0,1\rangle$ is a function such that $f(1)=1$, $f(2)=0$, and $f(3)=1$. $4$ is not in the domain (that's what 'dom' means) of the function. Thus the function $g$ is only equal to $1$ when the sequence $f(n)$ has an $n$-th term and this term is equal to $0$.
Apr 22, 2014 at 18:12	comment	added	Harry		Thank you, but can you explain yours a bit more. What does 'dom' stand for, i'm not familiar with the notation you used. If you can use the diagonalisation technique for this question, can you explain it using that?
Apr 22, 2014 at 17:49	history	answered	Mario Carneiro	CC BY-SA 3.0