Large Hardon Collider

[Woozie]

http://i1134.photobucket.com/albums/...shots/Nasa.jpg

LOL awesome!

Also, Cadsuane, sorry I haven't worked on your problem much. My first thought was to prove it by comparison test but I can't figure out how to get that to work. I'll probably look at it some more tomorrow morning if I have time.

[Cadsuane]

Nothing obvious comes to mind for limit and basic comparison, no. It has something to do with the fact that x^n is getting closer to 3^3n which is somehow related to (3n)!, but I can't see why.

[Ferion]

I've spent some time looking at your problem too Cadsuane and I'm really not sure what to do with it. When I have some more free time I'll mess around with it some more. This is probably completely far off but it's the only idea I haven't messed around with yet, could you have to look at some relations between the given series and the gamma function?

[Cadsuane]

I'm not supposed to know what that is yet!

[Mizango]

http://i1134.photobucket.com/albums/...shots/Nasa.jpg

HO.LY.COW. loool

[Woozie]

http://www.smbc-comics.com/comics/20110326.gif

[Altariel]

lol

[Cadsuane]

One important proveable limit:

(x^n)/n! -> 0 for any real x... which you can demonstrate with the pinching theorem for sequences...

Still not sure how that helps.

[Ferion]

Hmm and you're suppose to prove that the series diverges? With that limit my proof would show that series converges to 0.

Edit: The reason I say this is because if (x^n)/n! ->0 for any real x, then it's pretty safe to say that (x^n)/(3n!) ->0 for any real x since (3n!) > (n!). Unless I missing something very simple, in which case feel free to point it out.

Double Edit: Wait you mean (x^n)/(n!) ->0 as a sequence right?

[Cadsuane]

3^3n/3n! (as a sequence of natural numbers) converges to zero, so does 27^n/3n! and indeed 20000000^n/3n!. By itself that doesn't say anything about the limit of the sequence [(n!)^2(n+1)!27^n]/(3n)!, or anything about the convergence of the series (infinite sum) either.

I think it diverges but that's only because mathematica can't approximate a sum for x less greater than or equal to 27 for the power series [(n!)^2(n+1)!x^n]/(3n)!

[Ferion]

Yeah ignore my last post, made a very dumb mistake. I'll mess around with this some more tonight.

[Max™]

Because light travel at 299,792,458 m/s regardless of what your frame of reference used to be before.
Because you defined 1 meter as 1⁄299,792,458 of the distance traveled by the speed of light.

If Betelgeuse is 2 years away from you, the distance between you and that planet has to be shorter than 2 light year or you would be traveling faster than light. For that reason, the photon had to be emited less than 2 years ago. If you don't understand this, you don't understand the postulates of relativity (invariance of c).

Wow... yeah, you could be going FTL, or you could be moving slower through time...

Clearly I'm the dumb one here though for trying to point shit like this out.

How often do people say that the radius of the visible universe is "0 light year" instead of 93 billions light years? The idea is important in relativity, but not so much when we speak and try to understand its effect. Like I said, Euclidean distance is the only distance we are experiencing and that's why it's always correct to use it. The argument you're trying to have is stupid.

Wtf, this is why I give up.

Here, let me wiki something for you.

http://en.wikipedia.org/wiki/Non-Euclidean_geometry

Non-Euclidean geometry of spacetime
The scope of non-Euclidean geometry includes the spacetime theory of Herman Minkowski. This geometry substitutes a bilinear form for the usual metric distance. Concepts in this geometry refer to a hyperbolic angle rather than the usual Euclidean angle; for example the squeeze mapping moves these angles as does Euclidean rotation move ordinary angles. Instead of perpendicular lines, the spacetime geometry uses hyperbolic-orthogonal lines which determine hyperplanes of simultaneity. Foundations of a planar version of spacetime were explored, using synthetic geometry, in 1912 by Gilbert N. Lewis and Edwin B. Wilson in the Proceedings of the American Academy of Arts and Sciences 48:387–507. See the references for an excerpt, "Synthetic Spacetime", including definitions, 16 axioms, 21 theorems, and various corollaries by Lewis and Wilson.
Furthermore, hyperbolic geometry arises in special relativity as follows: an inertial frame of reference is determined by a velocity, and given a unit of time, each velocity corresponds to a future event from the origin that is the position of an observer with that velocity after the temporal unit. These future events form a hyperboloid, the basis of the hyperboloid model of hyperbolic geometry. Herman Minkowski made this connection on his famous paper of 1908.

Wtf is wrong with using a Euclidean measurement to describe a Non-Euclidean... no, no... nevermind, I'm tired of wasting my time on dickbags, peace out niggas.

[Kaylia]

Clearly I'm the dumb one here though for trying to point shit like this out.

You're not pointing out any shit, you're misunderstanding everyone by pointing out something trivial and useless.


Max, how often did you experience non-euclidean geometry in your world (excluding gravity)? It doesnt matter how fast you move, it's always Euclidean space all around you. The non-euclidean geometry only appears if you try to link the result observed by two differents observers who both live in different frame of reference.

[edit]
tldr: Light goes in a straigth line, and the clock next to you always tick normally. Where do you see non euclidean geometry?

Wow... yeah, you could be going FTL, or you could be moving slower through time...

Answer this question. How would you calculate the speed of a spacecraft that move at 0.9c. Are you going to uses Minkovski's or Euclidean's metric to figure the distance he covered?

Even better, how do we measure the speed of light? Do you think we need special relativity for this?

A single observer can always use time independent distance ( d²=x²+y²+z²). It's convenient in our frame of reference, and it's also the only distance that is meaningful for our brain. A time dependant distance (distance s²=t²-x²-y²-z² between events) is counter intuitive and will rarely tell you the informations you want to know unless you try to guess what the other frame of reference will experience. In the end, both are differents thing and have differents uses. Telling someone he is wrong for using one is retarded, especially when he used it correctly

[Chun Liroy]

Here, let me wiki something for you.


Wtf is wrong with using a Euclidean measurement to describe a Non-Euclidean... no, no... nevermind, I'm tired of wasting my time on dickbags, peace out niggas.

Did you really just...? LOL

[Lhyet]

Not to completely rag on Max but I am surprised that he, someone who is self taught in this stuff, doesn't step back and question his own understanding when everyone in this thread who has been studying these things in university and in jobs are telling him he's wrong.

I think Eliseos said it best:
Max's problem, in my opinion, is that he never admits when he's wrong. At least, not that I can ever remember. If you can't admit you are wrong about something, you aren't very likely to learn from it and become better at it. This is where the lack of any higher education hurts him, he doesn't have a teacher to grade him on what he does or knows right and wrong.

Anyway, sorry to continue this stupid derail again. The thread had gone back to a good state until he showed up calling all the people that know better 'dickbags'.

[Shiroikage]

Max's problem is that he is a goddamn asshole.

[Chun Liroy]

Max's problem is that he is a goddamn retard.

ftfy

[foopy]

i'm gonna miss max (srs).


though, i also miss vajra and leif.

[Cadsuane]

Alright I figured it out I think. In case you guys were curious:



If we can show:



at least for all n greater than some positive integer K, then the sequence cannot go to zero and hence the series cannot converge.

Let |x| = 27,

We have:



Which can be written as:



if alpha is greater than one for all n larger than some positive integer K, we are done. As it turns out:



It should now be clear that:



and we are done.

Remark: It also makes sense that this is the endpoint of the region of convergence. for x < 27, alpha would tend tend towards a number smaller than 1 as n went to infinity, which is easy to verify using l'hopital's rule.

[Eliseos]

Since Max is shitting up this thread again I'm going to unshit it. I posted this on my FB this morning but Boeing offered me an interview with one of their entry-level software engineering positions. It's with their defense corp, so it will be something in the fighter/missile system development. Miz it's in St Louis, so if I somehow get this position we're going to need to meet there this summer. I am so fucking excited that I even get to interview with them, making pew pew machines has been a dream of mine since I was a little kid.