AntiMagicMan

In[6]:= N[sin[10^40], 50] Out[6]= -0.56963340095363632730803418157356872313292131914787

From what I know of modulo arithmetic 0.5 mod 7 would not be defined. We have only had mod defined on the integers. If I had to make a wild guess to extend it to reals I would presume 0.5 mod 7 is still 0.5 .

How do you find out who leaves comments on the reputation system. I can't for the life of me work it out. Someone asked a question and I can't answer it.

A supernova? I don't know what a hypernova is. Well if you are lucky enough to see one, you will observe over the course of a few days that a small insignificant star brightens until it becomes the brightest object in the night sky, and then becomes dim again.

Speaking of Euler, how about the greatest equation in the whole of mathematics, e i pi 0 and 1 all tied up in one nice little formula: [math]\[ e^{i\pi } + 1 = 0 \] [/math]

I think most handheld calculators use taylor series approximation, there simply will not be enough terms for the sum to converge with a number that big.

I advise you speak in terms of frequency. Scientists like to use frequency because it is directly proportional to energy. Obviously you can see the upper limit on frequency is how much energy you are able to get into one place and convert into photons. Same with the smallest frequency, it depends on how little energy you can convert into a photon. Theoretically I'm sure it is possible to create frequencies larger than cosmic rays, but you have to realise these photons come from supernovas and supernovas are brighter than entire galaxies when they are exploding. I don't reckon we will be able to harness energy on that scale any time soon.

You need to go into preferences and set the translator to use LaTeX 2.09. I go to Durham University.

I must admit, I cheated with the TeX, I used MathType to create it. One of my friends can't decide which is best so he uses a tombstone with QED written inside it

I used Maple 9 and used evalf(sin(10^40)); and got -.5696334010 so i'm agreeing with Wolfson here. Mathematica 5 also gives -0.56963340.

I should have added that the last line is a result of the COLT theorem, but I guess that is pretty much implied. This was an exercise in our Analysis module.

Do you mean the smallest we can produce? If you want really small, then you need large particle accelerators, but do you want to know the smallest we can produce with big accelerators, or with more "everyday" equipment. Cosmic rays are not detected directly, their effects are detected in particle showers debris found in cloud chambers and other particle detectors. Basically the cosmic ray hits the atmosphere and a lot of energy is released in the form of electrons, pions, neutrinos and the like, and they come tumbling down to earth. The largest wavelength, requires the smallest energy, I am not sure if there really is a limit as to the largest wavelength. I'll have a look around and see what I can find out.

I'd be content with the fact that i'd know how everything works. But as a scientist that would be annoying, so i'd create a whole new universe, put myself in it, and use my powers to forget everything so I can figure it all out again.

That actually inspired me to make some, so I wanted to look for a proper recipe. And the first one I come across that makes any sense has a credit for YT, how weird is that. The net is a small place.

Theorem: For [math]\[ c \in R \][/math] [math]\[ (1 + \frac{c}{n})^n \to e^c \] [/math] Proof: Let [math] \[ x_n = (1 + \frac{c}{n})^n \] [/math] [math]\[ \log x_n = n\log (1 + \frac{c}{n}) \] [/math] Use [math]\[ \log x = \int\limits_1^x {\frac{1}{t}} dt \] [/math] So [math]\[ \log (1 + \frac{c}{n}) = \int\limits_1^{1 + \frac{c}{n}} {\frac{{dx}}{x}} \] [/math] We know that the area under the graph between these two points is log(1 + c/n) and we can pin down an upper and lower bound simply by taking the rectangles with width 1 and 1+c/n with height f(1) and f(1+c/n), then you get the inequality [math]\[ \frac{c}{n}\left( {1 + \frac{c}{n}} \right)^{ - 1} < \log (1 + \frac{c}{n}) < \frac{c}{n} \] [/math] which is equivalent to [math] \[ \frac{{cn}}{{c + n}} < \log x_n < c \] [/math] now it is true that [math] \[ \mathop {\lim }\limits_{n \to \infty } \frac{{cn}}{{c + n}} = c \] [/math] So [math]\[ \mathop {\lim }\limits_{n \to \infty } \log x_n = c \] [/math] by squeezing and all the remains to be done is apply the exponential function and we have [math]\[ \mathop {\lim }\limits_{n \to \infty } x_n = e^c \] [/math] QED!

I actually did a recipee search on the bbc food website. One of the first or second links leads to that. http://www.bbc.co.uk/cgi-bin/search/results.pl?go.x=0&tab=www&go.y=0&go=go&q=prawn%20crackers&scope=all&uri=%2Fhome%2Ftoday%2Findex.live.shtml 5th link on "results from the web". Just goes to show, you can find anything on the internet.

http://www.amigadude.pwp.blueyonder.co.uk/emmathechef/rcp000067.html Seems like you are a bit of a prawn cracker expert :|!

It produced from seaweed I believe. It is full of essential stuff that lots of things need to grow and it comes in powder form, naturally has gelatin in so it sets like a jelly. It is a pretty ideal substance for all manner of experiments. It is also used in japanese cooking I believe, so it is probally the very same stuff you saw in a shop.

If you remember that frequency is inversely proportional to wavelength by the formula f = c/lambda and that the energy of a photon is given by E=hf then you can see that as wavelengths get smaller, energies get higher. The highest energy photons we have access to come from cosmic rays, these can have energies up to 1TeV which would give you a wavelength of 1.24*10^-18 m, quite a few orders of magnitude smaller than that gamma radiation. I am not sure if there is a theoretical limit, you simply need to collide two particles (ideally a particle and it's antiparticle) at a very high energy to create high energy photons. But there is probally a practical limit in how much energy you can get into the original particles. Hope that sorts things out for you.

Oh bloody hell, my mistake, only reading the first two terms of a series is never a good thing.

Hmm, I have a low repuatation because someone thought I was wrong when I wasn't. Oh well, just shows the system isn't infallible.

Erm wait a second, someones maths has gone wrong somewhere here. It is indeed true that the series [math] \[\sum\limits_n {\frac{1}{{n^2 }}} \] [/math] converges to 1, but zeno was talking about the series [math] \[ \sum\limits_n {\frac{1}{{2n}}} \][/math] which is divergent (it is half of the harmonic series, which tends to infinity). But still there is no paradox because we all know it is possible to cover a finite distance in a finite time. Regardless of how much you subdivide 1 unit, it is still only 1 unit, and if you are travelling at 1 unit per second, after 1 second you will suprisingly enough have covered 1 unit.

Pedantic, yes . My basic point still remains, it is not harmful.

Believe me it is engineering. I know engineers at university and they study "stability of shapes, advanced equilibrium, compression and tension" and a lot lot more.

No, the sound is a result of the gas "boiling" out of the sinovial fluid and causing a change in pressure. It is really just a scare story that people use to try and stop people from doing it. Any damage will come from the wearing down of knuckle joints. But bone is a tough substance and it will really take a lot of wear and tear to affect the joint at all. Also it does not affect your chances of getting arthritus or any joint disease.