Let's discuss Mathematics

[ParadigmShifter]

I found a good link here:

http://everything2.com/title/Cauchy-Riemann%20equations

 

[Gamemaster77]

A, A>B, D>~C, B>C |- ~D

1.A>B ------------------------------hyp
2.B>C ------------------------------hyp
3.D>~C -----------------------------hyp
4.A ---------------------------------hyp
5.B ---------------------------------MP for. 1, for. 4
6.C ---------------------------------MP for. 2, for. 5
7.C>~D -----------------------------CPI for. 3
8.~D -------------------------------MP for. 7, for. 6

 

[ParadigmShifter]

Are you tripping on acid or just spamming?

 

[Gamemaster77]

That is a mathamatical proof.

 

[ParadigmShifter]

OK I'll humour you. What is ~ defined as?

 

[Gamemaster77]

~= not
>= implies
/\= and
\/= or
<=> = biconditional
MP=Modus Ponus
when from P>Q, and P you get Q
CPI=Contrapositive Inverse
where from P>Q you get ~Q>~P

 

[ParadigmShifter]

Right, not much discussion though.

I was thinking you were using > as greater than rather than implies and ~ as set complement which would make A>~C silly.

 

[Gamemaster77]

I am bored, solve this one, if you can(have know knowelege of your understanding of this, why would I, if not, then someone else do it)

A, A>B, D/\G, D>N, [B/\N]>~[~P\/~Q] |- P\/Q

 

[ParadigmShifter]

I'll have to bow out of formal logic I'm afraid. Fifty has some knowledge in that area IIRC.

 

[Fifty]

A, A>B, D/\G, D>N, [B/\N]>~[~P\/~Q] |- P\/Q

not gonna use your notation cuz i don't feel like it

6. (B&N)->~~(P&Q) 5, DeM
7. (B&N)->(P&Q) 6, DN
8. B 1,2, MP
9. D 3, simp
10. N 4,9,MP
11. B&N 8,10 conj.
12. P&Q 9,11 MP
13. P 12, Simp
14. PvQ 13, add.

Why the crap are we doing logic 101 proofs in thread that is supposed to be about interesting math.

 

[Fifty]

Speaking of logic, here's a problem for you gamemaster77:

Consider the following system:

Primitive symbols: infinitely many propositional symbols P, Q, R, S, T, with and without subscripts, parenthesis (or dots), and the single operator symbol "|". The rules for wffs in N may be stated as:

1. Any single letter of N is a wff.
2. If P and Q are wffs, then (P)|(Q) is a wff.
(No formula of N will be regarded as being a wff unless its being so follows from this definition)

Single axiom (in metalanguage... its a pattern for infinite axioms in the object language):

Ax. P.|.Q|R:|::T.|.T|T:.|:.S|Q:||S.|.P|S

Single rule of inference:

Rule. From P and P.|.R|Q to infer Q.

Now:



Prove: Q:.|:.Q|P.|.P:|:Q|P.|.P

 

[ParadigmShifter]

Why the crap are we doing logic 101 proofs in thread that is supposed to be about interesting math.

Hear hear

 

[Gamemaster77]

Sorry fifty I am yet to figure that out.

 

[ParadigmShifter]

Sorry for insinuating you were tripping on acid Gamemaster77. Logic is too low level for me

On topic, I found a nice online version of Euclid's Elements which has drawings, critique and everything.

http://aleph0.clarku.edu/~djoyce/java/elements/toc.html

 

[Gamemaster77]

That is fine ParadigmShifter. I only know basic logic fifty

 

[LulThyme]

Conjugation isn't a holomorphic function.

Found this, I'll read it after the Everton match

http://en.wikipedia.org/wiki/Holomorphic_function#Examples

Lord Olleus didn't say anything about holomorphic in his posts and, as dutchfire's example shows, the claim is false in general.

 

[LulThyme]

No, its best shown by an example.
Say F(z) :-> z^2 = (x^2 - y^2) + i(2xy)
so U(z) = x^2 - y^2 and V(z) = 2xy

so dU/dx = 2x
and dV/dy = 2x

ans similarly

dU/dy = -2y and dV/dx = 2y

Strange huh?

Another example is just confusing since dutchfire already showed a counter-example. Better than simply giving examples would have been to get your hypothesis straightened out.

 

[Ammar]

Strange huh?

When you consider the definition of complex differentiable it's pretty straightforward.

Basically, you can also consider a complex function as a function from R^2 to R^2. If it's complex differentiable it's Jacobi Matrix needs to have the form of a rotation times a real factor. That yields the Cauchy-Riemann equations.

 

[Mise]

Hey guys... Given two circles with radii r1 and r2 and and centre-to-centre distance d, how do I find how much area of those circles overlap (if any)?

Basically, I want a function of those three variables (or fewer, somehow), that doesn't involve integrals. That possible? I'll try and work through it myself in the mean time...

EDIT: Nevermind! http://mathworld.wolfram.com/Circle-CircleIntersection.html

Thanks Zelig!

 

[SS-18 ICBM]

Anyone know what this is about?