Shall I study Russel and Whitehead's Principia Mathematica alongside Godel's work, in order to better understand the context of what Godel did, or is reading PM mathematically pointless apart from historical context?
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Anonymous2008-11-15 21:09
Well, if you'd be interested in reading a 100 page proof that 1+1=2, go for it.
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Anonymous2008-11-15 21:32
Going through the introduction now; I also got a contemporary text on mathematical logic which may help.
I've checked out the first volume of PM a few times over the years for shits and giggles. The "1+1=2" anecdote is reproduced by Karl Sabbagh in his VERY poor ameteur text "The Riemann Hypothesis", which contains at least five very simple arithmetic errors. Mercifully, I read Derbyshire shortly afterwards.
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Anonymous2008-11-15 21:35
That book looks dry as dust man. Not to mention fucking hard to understand.
>"From this proposition it will follow, when arithmetical addition has been defined, that 1+1=2." – Volume I, 1st edition, page 379 (page 362 in 2nd edition; page 360 in abridged version).
379 pages and they still hadn't proved 1+1=2 (or even defined addition yet).
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Anonymous2008-11-17 0:57
Yeah but they were able to do it in an overly wordy and pretentious manner so what's your point.
How is it possible to make a mathematical proof too wordy?
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Anonymous2008-11-17 6:37
>>9
Now if you'd asked if it is possible to make a mathematical proof too wordy, that I could have done in a page or two. But no, you had to go ask for a constructive proof. I'm afraid that, as usual, the size of this post won't accomodate the proof that I have which is wonderful that I have discovered.
anon: ~$ /mode dis.chan.org/sci -m * AVERAGEANONYMOUS has set mode: -m
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Anonymous2008-11-17 17:57
>>9
My prof in graph theory was always on my case that my proofs were too short and terse, so once, just to piss her off, I spent three (typed) pages on one problem, verifying every little detail all the way down to associativity of addition.