Mathematical Girls - Gödel's Incompleteness Theorems

Why do I feel like I have read this somewhere before...

 

Is this a prequel to this series? -> http://vatoto.com/comic/_/comics/suugaku-girl-r1550

GODDAMN MOE CHARA FORCES TO READ THIS.

 

 

 

yeah... i hate math.. but moe.. moe.. moe

Thanks for the clarification about the list of systems, that's my oversight.

 

The Liar paradox was the one cited by the author, I agree that "system doesn't prove its own consistency" is more relevant, but I think that's too relevant in that it's actually one of the theorems. 

 

1+2=3 is an example of a conclusion from axioms (you do indeed also need 0+0=0, a + b* = (a+* and a* + b = (a+* or something similar), that's the only purpose it's serving there.

Sure enough I'm not completely satisfied by the author explanation at the end of the chapter; I know I am nitpicking, and explaining fully probably can't be done in a single page (and without equations) but I sure hope he explains more carefully in the next chapters... To start Gödel incompleteness speaks about first order predicate logic (as I understand it).
The list of axioms need not be finite, but recursive.

Goedel's first incompleteness theorem is, roughly speaking, "No system of logic powerful enough to describe arithmetic can prove all true statements regarding arithmetic, and hence itself", so it applies to first order logic among other systems. As for a recursive list of axioms being ok, bingo.

The example 1+2=3 is probably nonsense (need more axioms).

I agree; I think we also need s(n+1) = s(n) + 1 to prove this.

I also hope that this manga covers the second inconsistence theorem too, which I personally find a far more interesting result

Sure enough I'm not completely satisfied by the author explanation at the end of the chapter; I know I am nitpicking, and explaining fully probably can't be done in a single page (and withouth equations) but I sure hope he explains more carefully in the next chapters...

To start Gödel incompleteness speaks about first order predicate logic (as I understand it).

The list of axioms need not be finite, but recursive.

The example 1+2=3 is probably nonsense (need more axioms).

But more troubling, the liar paradox is more related to tarski undefinability of truth, than Gödel's incompleteness.

I closer analogy is the statement "this system is consistent" which runs into a different paradox (you may have heard of the story of a teacher announcing he will give a surprise exam in the week,

it cannot be the friday because by then it would not be a surprise, but then it cannot be on thursday, etc. I heard of this analogy from terrence tao's blog, which I recommend).

Ok.

I'm not a mathematical logician, but I know a bit of mathematical logic.

This is a pretty popular subject for nontechnical exposition, and I haven't read chapter 0 yet (I hope that is an easter egg, starting at 0, probably not though), anyway I am a bit skeptical, this is also a subject that is very easy to misrepresent...

So, here is to hoping.

this offends me >:C

How come? As a mathematical logician, I assure you the mathematics will be sound. 

 

And yeah there's not much to chapter 0. I trust we'll get to the fun in due course.

this offends me >:C

Its sequel of sugaku girl?

but i like artist in sugaku girl

I was more or less hypnotized by the title, so I had to come and have a look. ;o

It might turn out neat, though the initial chapter was pretty thin. I'll stick with it for a bit longer and see if it catches my interest.

This might be promising - depending on how the author does his math...

Though... Gödel... they've chosen one hell of a subject.

 

To conclude I will add one of my favourite quotes as it came to mind when reading the first chapter:

 

"The book of nature is written in the language of mathematics" - Galileo Galilei (The Assayer)

So this is where Love transcends all, even Math.

Oh yeah, I'm a match teacher so..
 

yeah !