the tree

No it isn't. This took me much less than a minute. As a further tip, in the first construction that came to mind for me, there were no elements that appeared in more than two of A,B,C or D. Well no, but I'm assuming your not a fine arts major, so I wouldn't worry about that.

Part ( a ) can easily be done simply by drawing a venn diagram, remembering to give each element a unique index (you know, just number then 1,2,3,4,5...). Once you've done that, for part ( b ) you can use your venn diagram to count the amount of elements in A-B and C-D. I'll tell you for free that |AxB|=|A|x|B|.

Yeah, even in developed countries people suffering with malnutrition from eating disorders are given full fat milk because it's a good way to take in a lot of calories very quickly and safely. I still don't think that milk and cookies are a good addition to a reasonably healthy person's diet. Take a look at WolframAlpha's analysis.

I don't really see how you've managed to go around your local grocers without noticing the 5 A Day posters all over the place, but it's definitely 5 A Day for fruit and vegetables. Whereas considering that most of the world are lactose intolerant, it sounds unlikely that a single serving of dairy would be "recommended".

When you say "need", what exactly do you mean? I might have had maybe one thing with cheese in it in the past week, and apart from that no dairy that I can think of (edit: no, I had a coffee with milk in a few days ago, make that two servings in a week or so). I seem not to be dying. Even for someone that consumes dairy on a regular basis, three servings a day seems excessive.

Dairy products aren't the best thing in the world for you. Water, fat and lactose - it's amazing how many people buy the idea of milk being so wonderful.

I have a physical notebook that I note down page numbers and quotes, URLs etc from stuff I'm reading. Sounds crazy when most of that reading is online, but y'know, it works.

That was a simplified account, shoot me.

That was not a joke on my part, that is what you are suggesting.

See, the question is interesting. The correct answer is not. The answer given by you, is wrong. I don't know how to make that any clearer. It is not a matter of opinion. It has nothing to do with Newton's third law. Photons have mass and are thus affected by gravitons. Gravitons have no such property that even suggests they may be similarly affected by photons. I would sincerly advise you not to have high hopes for anyone taking seriously the proposal that airplanes will find themselves lighter, simply by turning the lights on.

Okay, this bit starts with a vaguely interesting question "since gravity can muck about with light, can light much about with gravity?" Unfortunately, perhaps for you, the answer is no. No matter how big and shiny you make a sky hook, and no matter how many bells and whistles you hang from it - that sky hook will never be a crane. As has been discussed, nothing informative can be inferred from these videos. Here is a better idea, get a set of scales (like, ones for cooking, your mum probably has one) and put a penny on them. Turn the lights in the room on and off and see if anything happens. That way the result will be easy to see, perhaps that will be the most you'll ever benefit from watching a number not change. I know we all want flying cars, but I'd prefer my flying car to be based upon an idea that actually y'know, flies. THAT WEBSITE IS FOR CHILDREN.

Can't people just, like, not join the unions if they don't want to?

Thanks. So would it be fair to say, the particles can loose kinetic energy but are just as likely to pick it up again?

Well yeah, high repuation is fairly ambiguos - but it's usually pretty clear what a very low repuation means.

I don't think the amount of attention recivied can really be correllated to a positive reception. Good answers don't really need to be expanded on, whereas terrible answers warrant a quick rebuttal and that'll usually be dealt with by more than one member. The counter doesn't just serve the individual either, it's also a pretty handy method for newbies who want to work out who is worth listening to - like a sort of peer approved version of the Resident Experts scheme.

Also, the numerical counter that we've been discussing for eight pages. That as well.

I've been reading 'Mathematical Biology' by J.D. Murray (Springer, 1989, 1993). Particuarly chapter 15 'Animal Coat Patterns and Other Practical Applications of Reaction Diffusion Equations'. But my supervisor tells me that the Reaction Diffisusion model, whilst useful isn't considered to be accurate by contemporary biologists and the existence of morphogens is looking more and more doubtful. I am trying to use Reaction Diffusion Equations to look at the formation of patterns on butterfly wings, but would appreciate any knowledge on how much this model is thought to relate to the real world.

My friend, who has no scientific training but is otherwise pretty intelligent, texted me with: "Why is it when gasses collide they don't slow down at all? Shouldn't they eventually slow to the point that they become liquids?" I texted back saying that the only way they could slow down was if the kinetic energy was converted into some other form of energy, but I couldn't give a coherent explanation of why that doesn't ever happen - could anyone here help explain it?

Proofread for repetition, verbosity and points made that just aren't all that important. Get rid of weasel words like "I/some people think that...". For a very, very short essay, remember that examples/evidence/proofs/critical arguments aren't needed for every single point.

As far as choral hymns go, it's not the worst thing in the world. Nothing special either.

It's really fairly glaring to obvious, to anyone from any discipline, that science does not argue normative values. This all seems rather pointless.

@ajb, yeah that's what I meant. @im.no. according to the wiki article, the theorem applies to 2n dimensional sphere, so no.

Okay, I don't really know the language to describe this (like, at all). But if you had a dougnut where the hairs were say, pointing down on the inside and up on the outside - that should be well combed. Then another dougnut where the hairs were the other way around, the two could be intersected and then you'd have a surface with genus 2 that would still be well combed (does that make any amount of sense?). If any of that made sense then it should be possible to iterate that action for any genus. Am I at all on the right track?

I noticed from the graphics on the wiki that a combed torus was 'quite easy' but saw no expansion on that point. Do you know if other surfaces have been explored in much detail? I'd guess that not every n-torus could be combed.

There are a few posts with the odd 'lol', 'fyi' and 'ymmv' - it's not like we're completely devoid of abbreviations. I think the abbreviate-every-single-word-at-all-costs thing was a passing fad, and even though new initialisations still crop up every day, there is a general pattern of ease over brevity nowadays.