the tree

sin is a function, asin isn't (nor is it an algorithm) since it fails the well definedness property. The dirac delta isn't a function because it doesn't really work with the sets it's supposedly defined on.

I think I've said before that I think the thresholds should be more consistent. If all the boards with that type of restriction could be in one section, then that section could have the thresholds written right there.

Yeah, there's a certain amount of posts and being an active member for a certain amount of time. It's to prevent people from registering exclusively to use/troll those boards. From experience, it's the only workable solution.

I suppose a choice of forum skins wouldn't hurt. Anyway, I was thinking about a more creative approach to troll-management. Would it be possible to confine posters to the speculations forum as a step before outright bans? That would give them a chance to redeem themselves and perhaps appear less hostile than suspension.

There's also the option of a not-so-flat plane, with a what-do-ya-call-it, spherical cap type shape. But they also have very strange ideas about light: 'bendy light' as they call it. If light travelled really slowly and was affected by gravity (or an upwardly mobile earth) in a much greater sense than it actually is - so more like a bullet than a photon - then once 'shot' from far away at a reasonable height it'd eventually hit the ground.

Or some behavioural characteristic that you can derive those from. Buoyancy, displacement, urm.. weight?

Following the thread about homeschooling in Germany I thought it would be good to have a more general discussion on homeschooling and take a look at both sides of the argument. Please add any points or refute any of mine. Pros Child Safety: lots of parents want to keep their impressionable kids away from drugs and knives and peer pressure and keeping them at home is obviously going to help with that in the short term. If you view school as a dangerous place then it's natural to want to keep your kid away from it. Time dedicated to education: one teacher split among thirty children is obviously going to have less time to help an individual child than one parent taking care of three or four kids. There'd be time for personal attention and really making sure that work gets done. Cons Lack of specialism: unless the parents have degrees relevant to all the subjects that they are teaching, they aren't going to be able to offer as much specialist knowledge as a group of teachers and will in most cases be limited to teaching from the textbook which at best is just really boring. Lack of accountability: teachers are well regulated by external bodies, by their peers and by their students all of whom have the ability to call foul if a teacher does something seriously wrong. In an isolated environment such as home-schooling there could be a serious case of misconduct that just doesn't get noticed. Lack of social education: a lot of the things learned in school aren't the same as those taught - how to cope with other people (including those you don't get along with), how to deal with relationships and particularly how to resist peer pressure and dare-i-say-it how to not get completely screwed over should you get into a fight. All these things require exposure to a peer group.

Mathematics is difficult. If at any point you've got everything figured out, then someone will gladly come across some new questions to ask and new ideas to explore. Mr Skeptic is right, there is always more complicated maths. That's sort of analogous to the natural sciences as well, in that they are never finished.

You could argue that Christianity is less monotheistic than say, Judaism. Roman Catholics worship "the father the son and the holy ghost" who they do claim are all the same God, (but Hindus also claim that their various deities are the same God and lots of people call Hinduism polytheistic) as well as "venerating" Mary and thousands of saints.

No, we're talking about actual physical limits here.

Yup. Of a simple thing like a string of characters, it contains more information if it takes more data to describe it. This is an okay introductions. Kinda. There's an idea in biology that a lack of information causes a default towards symmetry.

So long as there is some restriction - that should prevent people registering primarily to post in the non-science boards, although maybe there'd be something to be said for keeping the policy consistent.

TeX is supported here ([imath]\mbox{try clicking here}[/imath]). I'll be honest: I was thrown off by the broken English and the attempt at typing in-line equations - just skimming through I didn't spot anything unusual.

It's worth emphasising the difference between an adjective and a noun. Say you have any given object: it could be hot or cold, shiny or dull, red or blue, spinning or stationary. None of those properties can really be separated from the object itself, and in fact two of them are forms of energy: thermal and kinetic. Thermal energy (heat) can be described as the amount that molecules are shaking and moving around within an object, the more movement - the hotter an object is. When molecules move around too much then a substance can't hold itself together which is why things melt and then evaporate. Also, when molecules are moving fast enough they can hit each other hard enough to break apart and reform, which is basically what a chemical reaction is, and that's why you tend to involve heat when you are cooking things.

Intestines, Yeah the solar system is kind of big. So much so that it takes around 4.3 hours for light to pass between the sun and pluto. However, the solar system barely qualifies as a drop in the ocean in the vastness of the galaxy, which itself is an insignificant blip in the whole of space. What like a , ???Hardly a scientific notation!! Mason is refering to standard form, in which 93,000,000 may be written as 9.3x107, which is in pretty common use. Crowned Conquern, when you moved into that glass house - did anyone mention anything about the throwing of stones?

You might want to work with what libraries give you as well, books. Oh, and what teachers give you, hopefully the wisdom to ask the right questions. And you'll probably need a pen and paper as well. Brains are good, but not really enough.

This. there is of course no real reason to pick one source. Some places have more wind and some places have more sun and some places have enough space to put a nuclear power plant. So it largely depends on context. I think a big problem with nuclear is that it can only be done on a big scale which means centralising power and I think that's something we need to get away from. Whereas a functional building can generate it's own power with smaller scale resources. I like anaerobic digesters a lot, because by coping with waste they kill two birds with one stone. (well, maybe they don't kill the second bird - but they certainly stun it). This looks hopeful.

I think it'd be worth generalising the question - the illness doesn't need to be directly responsible for violence. Say someone really didn't want to be under quarantine, to the extent that they broke out of incarceration, then should they be killed as a means of public safety? I would say yes but after alternatives have been explored:effective incarceration would be a start, rubber bullets, tranquillisers, then finally a well trained marksman - preferably not with a shotgun as a non-fatal shot could cause excessive pain which wouldn't be fair considering that breaking quarantine was their only crime. For that matter, does anyone know about the legal workings of quarantine orders? There must be some precedent on people breaking quarantine (hopefully not taken to the extent of lethal force).

The Bayesian answer to the Raven's paradox is a confirmation of a contrapositive is gives only a minor confirmation of the original generality - so while it increases the probability of the generalisation being true, only slightly so. And yeah, like Sisyphus said - the negate of 'black' is 'not-black', it isn't 'white'. Beyond that you can play with ideas like natural kinds and stuff.

This isn't really relevant. An anarchic group can have leaders and still be anarchic so long as that leader has no authority. "we're going over there and you're welcome to tag along" is a statement of leadership but has no implication of government.

Take reciprocals, partial fractions, yadda yadda - copying a method isn't going to help you with new questions nor is it going to help you learn anything. And seriously, look back at your textbook. Alternatively, just trying being sarcastic to your teacher and see where that gets you.

I'm sure it's obvious that we don't want to give you the full solutions. Teachers assign homework for a reason and it's not our place to undermine that. Hows about you tell us how far you've gotten? Oh, and maybe check if there's some information you're missing.

I'm fairly sure that Wikipedia lists all the well studied or interesting triangle-like sequences. There are of course other objects based around triangles like the Sierpinski triange (which can be aproximated by Pascal's, as you'd have read). If you're interested in that sort of number play then maybe you'd be just as interested in Latin squares and Magic squares. It might be the case that in your experimenting you've come across something that just hasn't been commonly formatted as a triangle before - novel representations can sometimes be very useful so keep with that.

Do you have any reason to think that a gravitational field would be in any way affected by a large amount of photons flying around? Think what that'd imply for a comet flying close to a star.