bloodhound

http://media.hugi.is/hahradi/fyndnar/skycutter40.wmv just wondering how does THAT work????? it doesnt look fake either.

this is a bit silly, but what is a difference between a metric space and a complete metric space.

actually i dont have a good understanding of rotating frames myself, we just did this in our mechanics module, and i find it very confusing expecially visualising between the inertial frame of reference and the rotating frame.

i dont know, at least i dont think so.[edit]come to think of it, what does magnetism has to do with gravity, in the macroscopic world anyway[/edit] explicit calculation gives [math]\pmb{g'}=-(g-a\omega^2\cos^{2}\lambda)\mathbf{k}-a\omega^2\sin\lambda\cos\lambda\mathbf{j}[/math] where i j k are right handed unit vectors fixed on the surface of the earth, radius a, such that j points to the north pole and k points straght up from the centre of earth. and lambda is the latitude. i.e angle from the equator. omega is angular velocity, whose direction is aligned with the north pole of the earth. so as you can see, if u are at the poles then u exprerience true gravity. i.e [math]\mathbf{g'}=\mathbf{g}=-g\mathbf{k}[/math] and at the equator u get [math]\mathbf{g'}=-(g-a\omega^2)\mathbf{k}[/math] so at equator and poles , gravity pulls towards the centre of earth, but with less magnitude at the equator.

A particle in non inertial rotating frame, will have the same equation of motion as if the particle were in in an inertial frame with 3 additional forces involving the angular velocity. If in am intertial frame S, we have equation of motion [math]m\ddot{\mathbf{r}}=\mathbf{F}[/math] the equation oof motion is the rotating frame S' is [math]m\ddot{\mathbf{r}'}=-2m\pmb{\omega}\times\dot{\mathbf{r'}}[/math][math]-m\dot{\pmb{\omega}}\times\mathbf{r}[/math][math]-m\pmb{\omega}\times(\pmb{\omega}\times\pmb{r})[/math][math]+\mathbf{F}[/math] These are the apparent forces on the particle due to the consequences of the non inertial rotating frame. The first term on the right is called the "Coriolis Force". the best example is that it defines the way water goes down a sink, according to where you are on earth. Also a particle dropped from height H will not land on the point directly below from where you dropped it. unless you are in the specific lcation on earth. So the apparent gravity we face is the not the same thing as the real one. i.e it doesnt point straight down to the centre of the earth. it points somewhere below the centre. the second term is 0 if angular velocity is constant the third term is what we refer to as the Centrifugal Force. A combination of these apparent forces in a rotating frame will create apparent gravity.

could you also give me an example of a uniformly continuous function on an open interval. As there is no point of that statement Mandrakeroot wrote if we assume that f is already assumed to be continuous on an closed interval.

well, the definition of compact i have been taught is that (in R^d) a subset C is said to be compact if every sequence [math](x_n) \subseteq C[/math] has a subsequence converging to a point to C A more useful equivalent definition is given as well C is compact iff C is closed and bounded. I know a set can be bounded set doesnt have to be closed, but I dont understand why a closed set doesnt always have to be bounded. Can some one give me a counterexample

could you give me some example of functions which are uniformly continuous in a open domain. does uniform continuity of a function imply other properties of that function as well?? like injectivity, linearlity etc...

i never came across "uniform continuous" . I know "uniform convergence of sequence of functions" .. but uniform continuous function? I get the extension of f to the closure of (a,b) so all you have to take is if f:(a,b) -> R then g[a,b] -> R defined by g(x)=f(x) if x in (a,b) [math]g(a)=\lim_{n\to\infty}f(a_n)[/math] where [math](a_n)\subseteq(a,b)[/math] and [math]a_n\to a[/math] g(b) defined similarly. is that correct?

mandrake. can u explain the bit. "then f has a continuous extension on the closure of A into R"

mastication - chewing moonlighting

isnt that just a definition of a limit

I have to say , i seen a really good custom made case, it was made entirely from glass, so it looked really elegant, it didnt have any wokny curves. only straight lines and edges. and thats about it. really liked it. probably the only one i have so far

so is he asking us to prove EVERTHING relating to limits of functions... good luck

If there WAS a flaws in mathematics that u suggest , then i dont think the great thinkers like Plato, Archimides, Pythogoras etc , or great mathematicians like Gauss, Euler, Cauchy, Newton etc. would have overlooked it so easily. but the "paradox" has already been solved by the famous Matt Grime. Remember you saw it here first. at ScienceForums. I will start selling "I talked to Matt Grime" t shirts soon.

my current desktop

not if u know where to get them for free

hey what about Red Dwarf. That was bloody funny I tell you

how come noone here is talking about mathematics. Mathematics graduates have consistently the highest starting salaries. and with a mathematics degree is relative easy to get a foothold in the financial sector, or management etc.

thing is , if anyone other than your fren or family saw ur pc, they wouldnt think ur were "cool". they would think you were some crazy obsessive person. For me "cool" is when you have an elegant design blended with simplicity and functionality.

nice pics tesseract, but you obviously forgot the best one. Vinnie Jones grabbing Gazza's nuts. for those who didnt know, vinnie jones used to play footie before he went into acting. OH AND WAIT. IT DOESNT END THERE!!

We can't even confirm if its a ball or not.

i had a go, u get horrible indices, so i couldnt be bothered.

i think he was talking about robots being controlled remotely by humans.

hmm. good logic mossoi.