/sci/ - Science & Math

Everything will be fine.

>>6458550
Gödel

What's the Gödel Prize worth? Can it be called a Nobel of computer science?

ITT: Kurt Gödel; how did he prove that you can't prove every true statement? anybody has gotten the actual paper? please, thank you!

>>6282033
>discounting epistemology and ethics

Just getting into this. WT actual F? Is "incompleteness" the end of logical thought? Does it make it all pointless? Are we to give up?

>>6124292

No honest Christian would ever go insane.

Oh wait...

Hey /sci/, I was able to pick up the complete works of pic related (all three volumes) for relatively cheap. However, I read through the introduction (as well as the background information) and realized that I really don't have the knowledge of set theory to understand his works very well. I read and enjoyed GEB: EGB. Is there a good stepping stone between that and Godel's essays?

I keep hearing how Gödel is one of the most important mathematicians of all time, rivaling people like Pythagoras and Euler and that in thousands of years time he will be remembered as one of the greatest minds to ever live.

But why? For his Incompleteness Theorem?

Eh, they are all bullshit but go with ontological because apparently it made sense to Godel and Leibniz.

=> "They Don't Think It Be Like It Is But It Do"
=> 1 + 1 = 2
Q.E.D.

>>5948913

>I like Islam, it is a consistent idea of religion and open-minded.

Kurt Gödel, smartest man ever who mathematically proved existence of God

>Implying everyone doesn't already know this
http://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems

>2012
>not choosing Kurt Godel

all of you are banned from /sci/ forever

>enemies want me dead
>constantly sending spies to poison my food
>only my wife can be trusted
>wife goes to hospital
>fine then, guess ill just starve

Kurt Goedel

Scrolls /sci/. Not one Science or Math related thread. Loads of religion, philosophies, stupid questions, even requests for books. This is basically /b/, and I hope each OP is banned for their stupid threads.

Posting one of my favorite videos for you guys, a lecture concerning math and prime numbers, but intended for a more general public to understand.

http://www.youtube.com/watch?v=PtsrAw1LR3E

Cool story.

Given Godel's first incompleteness theorem, when is it possible to ever have a system where all necessary truths are proved? What would be an example of a system where it is possible and where it is impossible?

logicians, mathematicians, i've got a question

how can it be, that if a first-order theory has an infinite model of cardinality K, then it has infinite models of every cardinality lesser or greater than K (http://en.wikipedia.org/wiki/Löwenheim-Skolem_theorem)
..but at the same time, if two sets are of different infinite cardinalities, then there is no bijection between them??

for example, take peano's arithmetic and the theory of real numbers..
peano's arithmetic has an intended model of infinite cardinality aleph 0
the theory of real numbers has an intended model of infinite cardinality greater than aleph 0
however, given the lowenheim-skolem theorem, then peano's arithmetic also has a model of cardinality greater than aleph 0, and the theory of real numbers also has a model of cardinality aleph 0
however, there is no bijection between the naturals and the reals, thus, there is no bijection between the domain of the intended model of peano's arithmetic, and the domain of the intended model of the theory of reals

how can this be?? is this skolems paradox? how is it not a contradiction?

You all small time. Enjoy your unprovable true statements.

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