studiot

Thank you John, that would make the problem easier. So that would make this first part you did correct. based on the above subsets

Well have you even attempted what I asked? It was a very simple request. Yet your response was to introduce a universal set, that was not correct, and not called for by that part of the question. P, Q and R are all sets of numbers. But they are not sets of the same types of number. In particular, as you have written them in Post#1, P and R are sets of real numbers Q is a set of integers. Back to my question The intersection of Q with R refers to a set that contains only numbers that are in both Q and R. Q contains all the odd integers, excluding 0, which is neither odd nor even. R contains a restricted interval of real numbers, which includes all the integers in that interval. So the intersection of Q with R boils down to all the integers, excluding 0, that are in the interval containing R. That is what I mean by stating in words. Can you now state this in symbols?

Why should I, when you won't cooperate with what I have to say? Your error is in the quote, look again at your first post.

You have gone against what I asked and again gone wrong. What I asked was designed specifically to help.

Individual elements (or parts of one) could be a (coordinate) vector. Unlike vectors, it is not required that all elements represent the same physical quantities, as in my stress tensor example. This means that you must have enough equations to handle different relationships.

If I take a £1 coin out of my right pocket the change in the number of coins is my right pocket is negative. That is I have one less coin in my right pocket. If I place that coin into my left pocket the change is positive. That is I have one more coin in my left pocket. The total coins I have remains the same. The situation with KE and PE is identical. This is because the sign is associated with the change, not the coin or energy itself. Conservation laws of coins (I wish) and energy require that one man's loss is another's gain.

Note also the specification when two material bodies interact. Then yes there is always a second opposing force. Note that Newton also included words to this effect. This extra specification is necessary because he needed to exclude the situation such as gravity in the space around objects. The force of gravity only comes into operation if a second object appears, but we cannot say there is no gravity around an object just because there is no second object there.

Exactly. There is an applied force (often called 'the action') This stimulates a second opposing force, often called the reaction. As I noted bfore they are exactly equal in magnitude, but opposing. Recognise Somebody's Law? Note also that this conclusion you have drawn, does not follow. That is it contradicts your first statement above and of course itself since it talks of creating a second force.

Yes of course and perhaps the drawer is locked or painted shut or something inside is sticking up and catching or....................... But none of these matter since they all apply the same force - just enough to resist your pull no more and no less. The whole point of a model is to extract only the important facts and discard all the rest, even though they are facts. The important facts are The drawer is a box You are applying a force by pulling Something is applying a foce by resisting. One drawer, two forces, no other facts matter.

Did you not say the drawer was stuck? So what is holding it back?

Good we are moving forwards. In fact we have the beginnings of a model - the object of this thread. When we make a model we strip away unecessary complications and try to extract one or a few simple principles. That is what we have done here. "A body can be held in place by two equal opposing forces" So we draw the block and two arrows to represent the forces. It does not matter how the forces are applied. It may be a wind blowing It may be that the block is made of iron and the forces is applied by a martian with a magnet It may be that Von Guericke had hitched his horses to the block (that is an interesting demonstration I will tell you about later) We have the beginnings of Newton's third law When two material bodies A and B interact so that body A applies a force on body B, body always B applies a counterforce on body A. In other words, in the material world forces always come in pairs.

Good one I hadn't thought of that. +1 for keeping with it. But what I meant was One force will push the block side ways. Two forces in applied in the same direction will push it faster but Two (equal) forces applied in opposition will hold it in place so it does not move. Do you agree?

I see there have been over 40 new views since I posted my belated response, but no one else has shown enough interest to post as well. This is a pity since we may have lost/driven away a potential member actually interested in technical matters, and also because as I said this is a nice question that demonstrates many useful ideas if one follows the the state and exchange variables around the cycle, by direct calculation rather than using the area of the triangle. All the numbers work out nicely and the integration to find the work for the leg AB is easy but very instructive since you will not find it as a standard method in any textbook. Any takers?

Which is why I suggested a simpler scenario. Yes, but I did not ask for a diagram (yet). Exactly, not unless I push it or Can you think of any other situation in which the block would not move sideways? (don't forget it is sitting on a horizontal table) I didn't mention density, why do you think this has anything at all to do with the situation? Please just try to follow detail as presented and don't introduce other material. I said we would move on to this one when you have the horizontal situation sorted. Do you think we have it sorted?

Timo was pretty well there. Whilst we normally resolve vector into x, y and z (or whatever) spatial coordinates, the fact reamins that it can also be (or is) a single entity, which is why I just said 'space'. If you have 2D or 3D space then you need to use a suitable differential operator (nabla or del), but the principle is the same. You have system in space and another in time that cannot solubly combine at the level of the first differentiation. The wave arises as a solution when you equate second differential coeficients. @iScience92, Why not keep it simple to a single space dimension, adding more does not add anything to the discussion. And please answer my question so we have a concrete example to work with. What is your equation for the wave?

This thread is about models. Models can be thought of as a representation of a particular situation (in this case a block sliding down an incline). I suggest you start with a simpler situation to represent. Say you start with the block sitting on a flat level table. Will it move by itself? Will it fall to the floor? when you have got this one sorted then tip the table so you can go on to an inclined plane.

Because there are two independent variables (time and space) and you have one equation for each variable or alternatively a single second order equation connecting them both. What is your equation for the wave?

I was going to ask for a link since I had not heard about this, but better still here is one http://www.bbc.co.uk/news/business-29004060 It seems that some sort of ban has already occurred/, with more proposed.

What you say about indifference rings true. http://blog.avast.com/2014/07/08/tens-of-thousands-of-americans-sell-themselves-online-every-day/?p_pro=1&p_vep=9&p_elm=55&p_var=%252Fpa%252Fen-gb%252Fother%252Fsecurity-report_licensed_90_security-report-news.html&p_ves=0&p_lqa=3&p_lqe=1&p_lsu=12&p_lst=0&p_lex=230&p_lng=en&p_lid=en-gb&p_bld=chr2&p_vbd=2021&p_hid=538e565f-0cbb-4412-be3e-a94f77ef2f2b&p_wei=-1.0&p_ram=1021&p_cpu=-1.0 Sorry about the 'ad' at the end of the blog, but it is a not for profit service

What I didn't tell you before was that the 10th floor was the restaurent. So customers only went to the restaurent because they were in the shop. Remove the other 9 floors (ie the shop) and what do you have? This is actually a real management example from the past, courtesy Stafford Beer.

That is far too simplistic a view IMHO. Try this: A management consultant was employed by a large department store to improve profit. Her study conscluded that the average profit generated per square foot was $1. However the 10th floor profit was $2 per sq foot. So she recommended that all the rest of the store be converted to selling the 10th floor product. Was she right?

The examples I gave all did change society, although by action and example as much as cash. There were many more. But who made those laws? The rich or the poor? And what if they are breaking them covertly? The rule of law is generally a good thing by surely that must also depend upon the laws themselves being 'good'?

I think every age has its share of philanthropists and patrons. The level of giving varies as does the nature of the support and the subject supported. eg Sainsbury and the arts Cadbury and better housing/ workers conditions Wellcome and medicine North and exploration records Nobel and many subjects

Of course greedy corporations (or their bosses I don't know which) don't need new legislation to perpetrate dirty tricks. For example the Dabigatran scandal and recent $360 million 'settlement' BMJ 26th July 2014 p15- 24