John Cuthber

In those cases I'd try changing the values a bit and see what happens. It will depend on the value, as well as the function. The simple approach would be that, near maxima and minima of functions, small changes in the input don't affect the output. However if the graph of the function is steep at some value then the effect of a small change from that value will be large.

Any number where the sum of the odd digits is the same as the sum of the even digits, is divisible by 11 so, yes. http://www.wikihow.com/Check-Divisibility-of-11 But I don't think that citing a wikihow page counts as mathematical proof.

These people say it better than I would http://www.lhup.edu/~dsimanek/scenario/errorman/calculus.htm http://en.wikibooks.org/wiki/General_Engineering_Introduction/Error_Analysis/Calculus_of_Error

"Interesting that the wikipedia article doesn't list diamond as the largest molecule, and says the largest one on record is around 100 nm." Interesting that it fails to notice that a typical DNA molecule is nearer a metre than 100nm. "Using your interpretation, a block of ice, or salt, would have to be considered a molecule. " No, blocks of ice are held together by hydrogen bonds, not covalent ones like diamond or quartz. Salt crystals are held together by electrostatic forces between ions. That's why I chose diamond and quartz. I don't see anyone asking for the molecular formula of diamond, so that's irrelevant. However the molecular formulae of polymers are often given as things like (C2F4)n and you could call diamond Cn if you really wanted a molecular formula. A diamond is a single molecule: it's not a very controversial point of view http://www.physicsforums.com/showthread.php?t=171339

It's complicated. The trig functions have errors that are related to their first derivatives. How good is your understanding of calculus?

Molecules are neutral collections of atoms held together by chemical bonds. "A molecule /ˈmɒlɪkjuːl/ is an electrically neutral group of two or more atoms held together by chemical bonds." from wiki The bonds occur throughout a diamond. All the bonds are the same, and all the atoms are held to eachother by chains of chemical bonds. A diamond is a single molecule, even if it's big enough to hurt if you drop it on your foot. Molecules vary depending on how the atoms are linked together. The simplest unit of diamond is a carbon atom, and yet the same is true of graphite. So, if the molecule is the simplest unit then graphite and diamond, having the same simplest unit, must be the same sort of molecule.

Here's an angle < you can split it into two right angled triangles by drawing a horizontal line through the middle of it. You can then calculate the opposite over the adjacent and you will get an answer something like 0.5 So the tangent of that angle (between one of those lines and the horizontal) is about 0.5 So far I have not mentioned any units. If someone told you that the arctan of an angle was 0.5 you could draw the angle. and then you could measure that angle in any units you liked- degrees, radians, grads whatever. Your calculator can't draw an angle for you as a reply to the question "what is arctan 0.5?" It has to give you a number. And that number will depend on whether you have set the calculator to deal in radians degreed grads or whatever.

It's a fundamental aspect of physics that you can't paint an electron purple. The electrons in an atom are all "mixed" and none of them can be specifically said to be an inner- or outer- shell electron. And the paper is entirely theoretical- no actual experiment has been done (and in a way, I don't blame them- high pressure fluorine isn't nice stuff to play with). What I'd like to see is a way to distinguish clearly between a Van der Waals compound* of CsF and F2 and this new "inner electron" compound CsF3. * something like this http://www.nature.com/nature/journal/v358/n6381/abs/358046a0.html

Long before mankind was here, plants grew. CO2+ H2O --> Cellulose etc. + O2 That's chemistry with or without human intervention.

Actually, there are plenty of molecules visible to the naked eye. Here's a fairly well known one. http://en.wikipedia.org/wiki/Cullinan_Diamond And here's a more accessible one. http://en.wikipedia.org/wiki/File:Quartz_synthese.jpg

It has several. http://www.oxforddictionaries.com/definition/english/tangent I don't think the one which is related to arctan is a line with the same gradient that touches a curve or an abrupt change of subject.

I'm fairly sure that for any given number base, n, it will fail for repunits longer than n. So, for most commonly used number systems, I can show that it fails. It's like the "observation" that 11^n gives you Pascal's triangle.

Someone should to check my arithmetic but 1111111111 ^2 = 1,234,567,900,987,654,321 1 2 3 4, 5 6 7 9 0 0, 9 8 7, 6 5 4 ,3 2 1 1+2+3+4+5+6+7+9+0+0+9+8+7+6+5+4+3+2+1 =82

Usually, but... Imagine I'm measuring the length of something then calculating something that depends on the tenth power of that length (it's an odd idea but I'm just illustrating the point) I measure it as 10cm +/- 1 cm That's two sig fig. Now I calculate the answer as 10 ^10 cm^10 (whatever that might mean) So I know the real length was between 9 and 11 cm So the real answer is between 9^ 10 i.e. 0.349 X 10^10 and 11^ 10 i.e. 2.59 X10 ^10 But those are not even right to one sig fig So you can't rely on the output of a calculation having the same number of sf as the inputs. It's usually easier for complicated calculations to work with the relative error, rather than the number of sig fig. So I measured the length to 1 part in 10. That's a 10% error. The clever bit is that you can combine the relative errors together to get a reasonable estimate of the error on the outcome. So, to take the case of the A4 paper. 21 +/- 0.1 one part in 210 or about 0.5% error and 296 +/- 0.1 is about 0.33 % error So the error margin on the area is about 0.8% So the area is 621.6 +/1 0.8% (or about 5 cm2) Imagine a square bit of paper instead. I measure the side as being 1 +/- 0.01 cm (so that's right to 1%) The side is between 0.99 and 1.01, so the area is somewhere between the square of those numbers 0.9801 and 1.0201 And a cube with that length of side would be between 0.97... and 1.03... So, I measured the side as being within 1% and the area is within 2% and the volume within 3%. For small errors you can say that the error in the calculated value is the error in the measured value multiplied by the power to which it's raised. (people who like calculus can prove this) This gives you a pretty good way of estimating the error on a calculated value without having to do much calculation. Even better- it lets you calculate how poorly you can measure each of the input values in order to get a required accuracy at the output.

The calculation of errors adn uncertainty is a lot more complicated than just counting significant figures. http://www.bipm.org/utils/common/documents/jcgm/JCGM_100_2008_E.pdf

It would probably be better all round if, rather than trying to do that, S1eep read up on the definitions of http://en.wikipedia.org/wiki/Scientific_evidence and http://en.wikipedia.org/wiki/Scientific_theory etc.

Would this help? http://humantouchofchemistry.com/the-chemistry-of-perming-rebonding.htm

if you take a look most countries have some sort of sordid history and have utilized continually use deception and propaganda.

Peracetic acid is a stronger oxidant than hydrogen peroxide. At the moment, your "evidence" for peracid formation is a pH measurement that won't tell you anything, made with coloured paper. Hydrogen peroxide will destroy some dyes used in that paper. You need to think this through better

So, the best you can do is say that we are "religious" in some metaphorical sense, but not an actually real sense. So, not actually religious. It looks like you are getting closer to the real world here. Now all you have to do is accept that at least some atheists are not actually religious (unless you use the word metaphorically- i.e. outsdide of it's real meaning.)

I'm entertaining myself until the mentalist turns up on telly. Hardly religious devotion. So, still wrong there.

I believe in no supernatural thing. the laws of physics are not something you "believe in" any more than you believe in chairs. You can describe them as "superhuman" if you like, but they are exactly the laws that let humans do what humans do. More importantly they don't control anything, because they have no "desire". They don't for example stop me jumping over the moon because they "choose to" do so. They just are. If the could "choose" to let me jump the moon then they would be in "control" but they are as much my slave as I am theirs. I have no faith in anything- I trust evidence but cautiously. I worship nothing and nobody. I follow no pursuit or interest with any great devotion. So, we have now established what I already pointed out. You don't understand what religion is in relation to at least one atheist (me). Would you like to get it wrong again?

That is apparently because you are not clever enough to understand the definition of religion. (I pointed this out earlier but you seem to have ignored it. post 98 if you want to check) In order to show that (in general) atheists are religious you need to prove it for (among others) the specific case of me. You need to show that my behaviour is religious. Your lack of understanding of this is nobody's problem but yours. But you might want to stop advertising it.

Weird, you quote the bit where I say "OK, they happen" And t the bit where I say " if some small country decided to take on China or the UK then it's likely to fail" But you don't notice that Iraq didn't invade the US, and you ignore the fact that,if Iraq's budget were 10% bigger and the US budget were 10% smaller, it would't have mattered- which was my point.

Nor is peracetic acid. Did you check the pH of the vinegar and the peroxide before you mixed them? Hydrogen peroxide solutions are often acidified because they are more stable in acid conditions. pH 3.5 isn't very acid for vinegar.