/sci/ - Science & Math

>>5413690
I was impressed by the puzzle too*, makes you realized that even if you're totally sure about a thing, you might just missing something.
I haven't delved into the modal logic definition of common knowledge, though.

*Terry Tao was too

I, personally, am mystified by the Church–Turing thesis, it seemingly being something different than math and physics. To me, I wonder if it might be the only real thing out there.

http://en.wikipedia.org/wiki/Bessel_function#Definitions

fun fact:
Whenever you see plots of function related to the Bessel theory, the oscillation seem to follow each other.
That's not an accident
http://en.wikipedia.org/wiki/Sturm_separation_theorem

Is cos(0) the same as -cos(0)?

look at the graph and you'll see that cos(-x)=cos(x) holds.

Well yes (without having checked all your formulas to the detail), there is a difference in the rules of univeral and existential quantifiert with respect to the and and or operations.

I'm fairly sure the sentences you describe are these on page 38, remark 2, in that script

www.math.psu.edu/simpson/notes/logic.pdf
A thing to notice is that you can express existential quantification via univeral quantification and the other way around.
See e.g.
http://en.wikipedia.org

/wiki/Existential_quantification#Negation

Bringing the formulas in normal form will reveal why it works out too.

You can prove it, eighter by the longish more general method presented there, and I've also seen a prove in the first Bourbaki book (which is so old that I'd not reccomend it anymore).
Conceptually, as quantification is not a mystery, you will understand it with easy sentences.

Btw. is there any reason you present these sentences with "in the domain D" here all the time? You never change the domain, so that subremark only makes the formulas more difficult to read.

there are four truth values to specify, namely r and s.
the statement
r -> s
is only false in the case "r...true, s...false".
Hence
-(r -> s)
is only true for this case, so you have
r
-s
You already have
-p
so
p v s
is false
so
-(p v s)
is true
so
r ^ -(p v s)
is too.

This is only a formation sequence, but it shows you can concluse r and not s from -(r -> s).
I think.

http://www.physicsforums.com/showthread.php?t=82552

Formulate the principle of relativity and what distinguishes it from all laws being Lorentz invariant.

Also, douchbag answer:
Sure, if there are no laws or if "spacetime" is zero dimensional.

http://en.wikipedia.org/wiki/The_art_of_being_right

>>4305362
depending from your approaching angle, a good understanding of the Lagrangian formalism or field theor, especially Noether currents are of value. What is a fair amount of QM? People use Ryder, Peskin & Schröder or Weinberg if you're not afraid of math

http://www.youtube.com/watch?v=NWUFjb8w9Ps

Is Khan Academy an interactive site? I only know the videos.

>>4025639
It's non-trivial and has to do with how (in what norm) the series converges.

>>4017504
>change in the electron's energy
Once you use the time independend Schrödinger equation there is no change in any observable/expactation value. (without observer interaction).

As soon as you consider a compact domain (like in this potential case, where the wave function is modelled to vanis at 0 and L) there are descretely many solutions to your equation (typically indexed by an index n) and to each of these, there corresponds and eigenvalue E_n.

>>4001451
Z_2 is "{1,-1} and ·" or "{0,1} and +", explicitly

1·1=1,
1·-1=-1,
-1·1=-1
-1·-1=1

or

0+0=0
0+1=1
1+0=1
1+1=0

with 1, -1 they mean the first representation, but it's isomorphic to the second one. Using +, i.e. the second one is sometimes more natural because it suggests communitivity and is natural in Z_n=Z/nZ in general.

Now G has 6 elements, H has 3 so G/H has two. There is only one group with 2 elements, namely Z_2.
So you have to group 3 objects to one element (namely H becomes e or "1" or in the other representation "0") and the other to the other element in Z_2 (namely a or "-1" or "1").