studiot

Don't rely on the timestamps here, they are often inaccurate. It was not a mistake just language difficulties, don't worry about it, no one will complain as you are obviously doing your best to communicate. I did say keep doing this as it will help and an English course will also help if you have time for one. Cheer up and concentrate on trying to put over what you want to say about mathematics.

Firstly you link doesn't work properly in all browsers. Secondly, it doesn't work as expected in Microsoft Edge in Windows10. Your example contains 6 data points, enough to establish six unknown coefficients. Yet your example insists that the data is from a third degree polynomial, whatever degree I ask for. So is this a cubic spline approximation or what?

All of these. Keep asking questions it will help your English. For instance I understand your question above, but it was not good English What sort of difficulty do you mean? What kind of difficulty do you mean? Is good English. Sorry for my spelling mistakes in my posts above I hope you notices I often write form instead of from.

I have the 1989 edition of 'Introductory Functional Analysis with Applications' by Kreysig. You may find the treatment of waves from a functional analysis point of view by 'Applied Functional Analysis' by Griffel of more interest.

I still don't see an answer to my question. Functional analysis is the mathematical study of mathematical spaces and the maps between spaces. As such Fourier analysis is included. Fourier analysis is the mathematics of periodic (wave ) functions. When the fourier sequence is finite the map is form the space of continuous, continuously differentiable functions to itself. When the fourier sequence is infinite the map is from the space of continuous etc functions to a space including discontinuous functions eg square wave or pulse that I mentioned before. I'm sure there is a language difficulty so you sould include more mathematics in your questions. Those responding will have no trouble with this.

I suspect your 'problem' lies here (underlined). If you do not understand IMHO you should be heeding Ed's sensible safety advice.

What does this have to do with functional analysis? Note. 1) Of course you can see the phone signal waves with a device - it is called a phone. 2) The phone signals are pulses not waves.

Yes I agree the logic is flawless. But I don't see it as the problem. Some years backalong, where I live, we had a former leader of the liberal party in our area before he was prominent. I heard him speak passionately putting the point "We don't need the nuclear option now" When he was opposing the development of a new reactor at Hinckly Point, our local nuclear power plant. The replacement reactor was shelved for decades and now we are witnessing one of the biggest fiascos in finanace, politics and engineering about the current attempts to replace the old one. Those who have lived that long have spent the best part of a century watching a similar struggle to not build an even better clean energy device of even greater capacity here in Somerset, but that is another story. It seems to me that, all too often. the bigger the project the less the plain common sense that goes into it.

I seem to remember that the book you mentioned was general chemistry. From university level you need more area specific books for different topics within the subject. With all the modern web resources, perhaps you students don't use books these days but here is a brief bibliography. Chemistry a structural view Stranks et al Cambridge University Press Chenical Binding and Structure Spice Pergamon Solid State Chemistry Smart and Moore Chapman and Hall and the grandady of them all Structural Inorganic Chemistry Wells Oxford University Press

Interesting paragraph. Here is a supposed conversation that took place in 1919 at the conference where Eddington presented the first experimental confirmation of (general) relativity. Physicist, Professor Silberstein, "Professor Eddington you must be one of the three persons in the world who understand general relativity" Eddington "Smiles" Siberstein "Don't be modest, Eddington" Eddington "On the contrary I'm trying to think who the third person might be"

A century or more ago the aether wind may have been a plausible explanation, but since that time there have been so many confirmations of relativity in so many different directions, over so many different distances, large and small, that such an explanation cannot now be supported.

Yup +1

I already offered you this but you don't seem to want to discuss it. Take our Earth with its lines of longitude. 3 dimensions All the lines of longitude end at one point (well 2 actually), a pole. Now open out the surface to become a mercator map. 2 dimensions But all the lines of longitude are still there However they no longer meet but reach the end of the map at different points. Do you want to discuss this further? I mentioned the word manifold, if you understand what this means please say so as this is an example.

Reading post 88 Methinks our learned friend has been drinking too much from his desert still.

I think this discussion has really brought out the limitations of the rigid A or NotA brand of logic. So many of the terms support multiple interpretations and/or suble nuances of meaning. Worse the moment we introduce explanations we introduce more terms to have shades of. The meaning of measureable or observable for instance, I think my examples have shown that even the concept of existence has such range of meaning and cannot be simply described as exists or not exists. Another muse arising from another thread where we were discussing the meaning of singularities. We are all happy with the function y = x2 rising ever more as we increase x and noting that we can never 'get to the other side of that infinity' I don't think anyone would call that a singularity, because we can see that we can never reach it. But consider the function y = 1/mod(x). This has a singularity at x=0 (note I do not say at the origin as is often said and is strictly incorrect) But we can bracket or get to both sides of this curve so we regard this infinity as a disturbance of some sort in our otherwise controlled number line and call it a singularity.

Wow what resources are available today. This stuff is mind bending on first reading. You are correct with your first example and you seem to have picked up the rules for numbers of atoms per cell. 1) An atom lying totally within a unit cell belongs to that cell only and contributes one. 2) An atom lying on the face of the cell belongs to two cells equally and counts as one half. 3) An atom lying on an edge is common to four unit cells and therefore contributes one quarter. 4) An atom at a corner is common to eight unit cells and therefore counts one eighth. Your second example is of the Nickel Arsenide (NiAs) structure with repeating ABABAB etc units. The unit cell is discussed in this powerpoint, page 8,9 http://homepages.abdn.ac.uk/j.skakle/pages/y3-2002/3lec6.ppt and again in this pdf from page 46. http://www.chem.uci.edu/~lawm/253%202.pdf You can also play with these interactive sites. http://www.chemtube3d.com/solidstate/_sync(NiAs).htm http://www.chemtube3d.com/solidstate/_NiAs(final).htm

cladking You're going toneed to explain this to me. I'm sure if you're right then I'm wrong. Of course. People copy non existent characters in fiction books, films and video games, as well as real ones in the news, and other non-fiction material. People searched in vain for Atlantis, the holy grail, the aether and the philosopher's stone. Thank you for the answer. As with strange's comment that these any electron in these states has finite energy, I don't see that either of you questions are relevant. The OP question (proposition) is that infinity does not exist in the real world. Not whether we can observe it, or whether the states (if they exist) are occupied, simply that they are available. In the absence of a better definition from the OP or anyone else, and I have asked in this thread, I am equating availability with existence.

Hello, Saby and welcome. The first term in your expansion is [math]\frac{{{\mu _0}I}}{{4\pi r}}\oint\limits_{} {dl} [/math] Remember what dl is. It is the physical spatial displacement vector. (not the electric displacment vector D) When taken round a complete loop it must end up where it started. That is the total displacement must be zero. so [math]\oint\limits_{} {dl} = 0[/math] I didn't get why the last thing (the nabla opened thing) was zero... If you want to display math here go to this (free) site and type it in. It will generate either Latex or a gif for you to paste in. Edit forgot the links, sorry. http://www.sciweavers.org/free-online-latex-equation-editor or https://www.codecogs.com/latex/eqneditor.php

Yes I quite agree and I was just thinking of posting to invite cladking, who introduced the question, to say what he means by reality and exists. I was thinking about a test for existence and came up with the question Can something that does not exist interact with/affect reality? I thought I had it but then I realised that non existent things do indeed affect reality.

Look up mica, graphite & clay mineral structures. The layered structure affects physical and electrical properties.and produces anisotropies in these properties. Graphite is used as a lubricant. Find out if the bonding in graphite is ionic or covalent then look up its electrical properties Mica can be cut to ultrathin sheets Clay minerals have a hugely rich structure and hold pore water in soils.

Yes , you said that before and it is quite true, but I don't see how that is relevent? For instance how many natural numbers are there? Yet every one of them is finite. Consider further Enumeration is now considered one of the basic physical 'dimensions', along with mass, length, time, etc. Energy is not so considered.

Of course, but the original purpose of this model was substantially more exacting than the question we are discussing here. Surely it is enough to know that 1) An electron can be removed form a hydrogen atom 2) Whiilst bound within the atom the electron has a finite number of energy states available to it (neither the exact number, nor their exact values are relevent here) 3) Once the electron has left tthe atom, leaving a hydrogen ion behind, it is in a continuum and has surely therefore has an infinity of states availble to it. So is this not an example of physical realisation of infinity?

Thank you ajb, I see I did not explain myself very well since you have picked up far more complicated cases than I envisaged. I was not thinking of anything so complicated as the band structures in solid state physics, just a single atom or molecule, possibly the simplest ie hydrogen. In any event band structures still have a finite number of states available. I was just thinking about the morse curve http://www.chemicool.com/definition/morse_potential.html and the ionisation energy, when the electron breaks free of a simple molecule to form an ion and a free electron, which is in a continuum of energy states.

ajb, This really is the key point and one I seem to have to keep making (but not for your benefit). It does not matter if a theory gives us infinity for a 'value' of something we would like to meassure, which is usually the result of taking limits either in terms like 1/r or in terms of power series, this is interpreted as 'pushing the theory too far'. Singularies can appear in very simple models, like electrostatics or much more complicated theoreis in quantum field theory. They just show that the theories we have are not complete and that physics beyond these models is needed. ajb, I would really value your comment on the situation posed at the end of my post#56? ajb In truth it seems to correspond to the scientific standards of this forum and in particular the quality of the posts of the members. However, collecting lots of negative points quickly is usually a sign of poor attitude and civility. I tell you this because we know that collecting negative points is an indicator of a member quickly becoming banned for breaking the rules. I do not wish that to happen to you. Once again, +1 for displaying far greater tolerance and patience than I can.

Yes seems a reasonable if pessimistic summing up, with the exception that many think the underlined words are obvious. What's more because reality is more that our (best) models (or to put it another way reality is our best models and then a whole lot more) it surely must include infinity since the models do so.