studiot

Or as 10cc put it

So you do not wish to answer the question I asked. Fair enough, I wish you well in your quest. I will leave you with the observation that in addition to not defining any of the terms I asked for, your last post introduced yet more undefined terms that for everyone else have different definitions and follow different rules .

At this time I don't have any 'other concerns' because I'm sorry but this line is meaningless misuse of symbolism and I don't know what you are trying to say. I understand the first part: For every element, X, of the set of real numbers, R, and with the sole exception of zero, It is the next part of the statement that is unintelligable. What is x, what is (x,x) and what is the equals sign doing there? Please state what you mean in English, then we can sort out what symbolism can be used and proceed. I have given you an example above. There is nothing you can state in mathematical symbols that can't be stated in English, indeed the first time any symbolism is introduced it must perforce be stated in English first. Without this I am reduced to scratching around trying to guess what you might possibly mean by the statement. Thank you for the + point but I would rather you had answered the question I asked in that post, which concerned my latest guess. This is important, and also answers Strange's point. I was wondering if your (x,x) was like a computer address. An instruction in machine code might be to go to such and such an address in memory, Take what you find at that address Do something with it, say double it. The point is the separation of the address and the data that is held in that address.

Thank you for your reply, I see you did not catch my meaning. To able to place all the real numbers in a table is equivalent to counting them as every place or pigeonhole in any table can be given a unique (serial) number, which is another way of saying that you cannot put all the real numbers in one-to-one correspondence with the integers. The real numbers are not countable. The fact that there is at least one that doesn't fit into any table was Cantor's original proof that there are more reals than integers. There are just too many real numbers so a table containing all of them is wishful thinking. However is your idea equivalent to saying that every number fits into a unique pigeonhole which may be referenced by a column and row reference? This is what database designers call a flat table.

A lengthy discussion about belief would be off topic here, but thank you for your reply I find it perfectly reasonable. The topic of this thread is energy and energy conservation. I was disappointed that you put less effort into reading that part of my post and missed several vital points, or at least you did not acknowledge them. I think the best way to achieve an understanding of energy is to include some historical material since the history of the subject has left us with some mixed up terminology often due to historical misunderstandings such as the (incorrect) belief that heat energy is a substance they called caloric. It took the best part of a century to dispel this notion. It should be noted that Newton did not work in terms of energy and energy laws. He discussed something which we now called momentum. Energy did not start to surface till the century following Newton, and conservation a century after that. There is also more to Work and its relationship to energy than has so far been presented here. I am quite happy to offer a reasoned development of these topics, but only if you will take more notice than you did of my first post since the production would involve significant effort on my behalf and perhaps yours. Understanding is more than belief, but does require this effort. @Mordred. 1919 Physics huh? Youngster! No wonder your avatar looks more sprightly than mine.

One problem I see is that there exists no table large enough to hold all the real numbers. So are you restricting this to integers?

I think that energy conservation appears in many guises, but only works if you chose the appropriate version and apply it corrrectly. I also think that energy is not a substance that can be isolated from a body or passed directly to another body. I am glad you acknowledge that there are various forms of energy, but beware they are not absolute. Here is a question for you to ponder. Water is impounded behind a dam 75 metres in height. A pipe leads water from the bottom of the dam through a turbine to a discharge pond. Thus the potential energy in the impounded water does work operating the turbine and in turn an electricity generator. It is easy to calculate the maximum available (potential) energy of the water in realation to the height of the dam. Or is it? Suppose I now tell you that the pipe leads 6 kilometres down the valley, a further dop in height of 150 metres, before it reaches the turbine. The dam and the source lake are the same as before but what is now the potential energy? As a matter of interest, you have called yourself the Believer. What exactly is it you believe? Science is not about belief.

I am assuming that long enough time elapses between the capture of the molecule and the moving of the wall for the thermal radiation exchange between the walls and the molecule to equilibrate. Once equilibrium has been established as there is only one molecule it must travel at constant velocity - there is no group average to consider - and that all wall collisions are elastic. As far as the Daemon is concerned I am assuming the usual frictionless piston arrangement and reversible movement. So the volume of the box is reduced. However the Laws of Thermodynamics can't be cheated that easily and work is still done. Yes it will be reversible work under these conditions. Goodnight all until tomorrow.

Like the Daemon, I was getting bored with all the politics threads and this thread was inspired by a question elsewhere where the poster had trouble understanding the difference between the statistics of geometric configurations and the statistics of energy levels as applied to entropy. So I re-tasked the Daemon as follows. Consider a rarified gas and let the Daemon take an empty box with a moveable side and capture a single molecule inside the box, so there is nothing else in the box. The molecule bounces about inside the box as expected. Question 1) Is the entropy any difference when the molecule is on the left hand side of the box, the right hand side of the box or in the middle? Question 2) Let the Daemon move the movable side in a bit, in the time the molecule is elsewhere and bring the side to a complete halt before the molecule hits it. Has any work been done? Question 3) Would anybody like to make any other comments on the Thermodynamics of the situation?

Yes, 8 would be the correct successor of 7. But if (7+h) is a successor of 7 then so is (7+0.5h) and (infinitely) many others. The point of successors are that they are unique so that Every number has a successor, no two numbers have the same successor. Two other axioms are necessary. 1 is a number (I learned 1, modern treatments seem to use 0 which was originally avoided because it brings other difficulties with it) 1 is not the successor of any number. These four axioms are enough to set up self consistent finite and infinite sequences (originally called successions). Incidentally set theory is normally reserved until University in the UK and it is not needed to introduce sequences. By the way to get the infinity (and other useful symbols) on Windows, type 'charmap.exe' into the windows run/search box depending upon which version you have. Select the infinity symbol chose copy Paste in the symbol ∞ Selerct the symbol and change the font size to suit ∞ is 36 @Old Chem Engineer. You find the reason why we need a sum ( including to infinity) to work with to replace an unending sequence is that the unending sequence has a value if the sequence is convergent. If that is the case we can do arithmetic with the sequence, and justify term by term actions

Not really. The sum could be divergent for numbers greater than 1. The rules for manipulating infinite series only allow convergent series.

Even in high school mathematics it is not a limit it is a sum. There is a considerable difference.

This is a logical red herring. 0.9 recurring is an unending decimal number with no 'successor'. Successors refer to the construction of the positive integers, by one particular axiom scheme. Note that axiomatic schemas for arithmetic are not taught at the elvel you requested a reply. A good (university) book which uses the successor scheme and comapres it with others is The Number System by Professor H. A. Thurston.

Truncation is not necessary, you just have to correctly apply the rules taught in high school for sequences and series. Again it is a question of following the rules, limits are for sequences, when we talk about series we use the rules for convergence. So the limit of the following sequence is zero [math]\mathop {\lim }\limits_{n \to \infty } \left\{ {\frac{9}{{{{10}^n}}}} \right\} = 0[/math] That is [math]\frac{9}{{10}},\frac{9}{{100}},\frac{9}{{1000}},\frac{9}{{10000}} \to 0[/math] However the infinite series is convergent so has a sum to infinity [math]\sum\limits_{n = 1}^\infty {\frac{9}{{{{10}^n}}}} = \frac{9}{{10}} + \frac{9}{{100}} + \frac{9}{{1000}} + \frac{9}{{10000}}............. = 1[/math] As John showed.

The question is inderminate because it depends upon the meaning of the phrase 'total ingredients'. Do you mean 8 sandwich fillings? If so, is there only one filling that includes ham? The basic probability, assuming every sandwhich has one filling and there are an equal number of sandwiches with each filling is 1 in 8.

It sounds like you are looking for what we now call the Archimedean spiral (He studied spirals in general and published a book about them). This one moves away from a fixed point with contant speed along a line which rotates with fixed velocity about the fixed point. If we set the origin at the fixed point, the equation is [math]r = a\theta [/math]

Nice one John, I was going to say something complicated but yours is better. +1

Have you heard of casting out nines? https://en.wikipedia.org/wiki/Casting_out_nines

We can offer hints so if you don't know where to start here is a hint epimers are special types of isomers. Here is the original example. You should compare this with an example of otho, meta and para isomerism. Note there are three of these but only two epimers. Find out which of all these are optically active.

Good reply fiveworlds, +1 , but will the manufacturer actually cooperate?

So you are using the word radiation to describe a geometric pattern, as in "the spokes of a wheel radiate from its hub". Can I assume this is not meant to imply any continuous generation of an energy stream emanating from the magnet as radioactive radiation or EM would be?

Thanks but that doesn't answer my comment that the forum software must create a count to come up with the number that is displayed to all. If say the displayed post count number is 20 are you saying that the claim is members of a scientific forum or even 5 year olds, are incapable of counting the actual number of posts and finding out that only 15 are displayed? Or does the displayed post count number actually with the numeber of posts displayed? The moderators are quite assiduous in displaying a notice to the effect that some posts have been hidden. In any event, is it beyond these super programmers to keep several running totals for whatever different purposes they want?

I'm hoping this was not part of your response to me, specially when you mention in the same breath. Anyway I asked for clarification of your phrase "centrifugal magnetic radiation" and I take it that the words between the above quotes form some sort of response. For your information I am quite comfortable with Fields in general and EM fields in particular. I am not aware that a phenomenon that could be described as magnetic radiation (centrifugal or otherwise) can be isolated. Could you please offer an example of a radiation that is purely magnetic? So far as I am aware, the only radiation emitted by permanent magnets comprises some low level random radiactivity from material impurities and the usual black body radiation, appropriate to its temperature. Neither of these could be described as magnetic radiation.

Well here are my thoughts. 1) It must be possible or the program could not provide the information about the number of replies. 2) Are we to understand that the program authors never intend to issue any updates? 3) Even Microsoft admitted it was wrong over the start button fiasco.

I have been trying to find the foreward in a book I have where the author states The Scientific Method is the collection of data about the real world and its organisation in a rational structure.