Talk:Diagonal lemma
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[edit] unsure about proper LaTeX use
I made some of the equations into LaTeX form, but I'm unsure of how to format the quotes. I was taught to open and close quotes (in text mode) with ` and '. Unfortunately, the backquote character produces a rendering error. Instead, I used
- T \vDash t = ''B''
which produces
That aint' right, obviously. What's the right way to get quotes in an equation? Twinxor t 21:17, 8 April 2006 (UTC)
- Actually, using ``B" (a double quote on the right) works in LaTeX, and it seems that's what most people do if they need quotes in an equation. Unfortunately, as you noticed, it doesn't work in MediaWiki. At this point, I would suggest asking on Wikipedia_talk:WikiProject_Mathematics, as that will attract the attention of some people very savvy in this kind of stuff. --Chan-Ho (Talk) 08:17, 9 April 2006 (UTC)
- Damn, where was all this expertise when I ran into excatly the same problem? :) I spent ages reading all the documentation and concluded that there is no clean way of doing real quotes in equations, if you can't escape out of math mode temporarily. Stevage 14:53, 7 May 2006 (UTC)
[edit] Proposed new proof
Proof. Substitute the code number of A for x in A(x) and obtain the sentence A("A"). Let Diag(A) denote this sentence, called the diagonalization of A. Diag, the diagonal function, is representable in T because Diag can be proved computable and by assumption, all computable functions can be represented in T. Let D(x) denote the T representation of the diagonal function. Consider the sentence A(D(x)), which asserts that the diagonalization of x has property A. Now let B be the diagonalization of A(D(x)), so that B is the sentence A(D("A(D(x))")). Hence B has the form A(t), where t is the term D("A(D(x))"). Clearly,
(1) 
But t denotes the diagonalization of A(D(x)), namely B. Also,
(2) 
because B is provable in T. Substituting (2) into (1) yields:
QED.
This proof isn't so much "new" as "reworded". I want to give experts in the area an opportunity to twiddle this proof until they are satisfied. I have interchanged D(x) and Diag(x). The shorter notation should be used for the function that can be an argument of predicates.
Where can I find a proof that Diag is computable?202.36.179.65 23:54, 16 August 2006 (UTC)
[edit] Questions about proof
Why is B provable? The current proofs just assert this without explanation. Why is provability of B necessary to show 
? - 72.57.120.3 09:43, 7 September 2006 (UTC)
