studiot

Only the users - It is a democracy. Yes but it doesn't change it. The silent e means that the previous vowel or sometimes consonant has its 'proper' sound - That is the sound of its name in the alphabet. This is brought out by my examples. Though, like other rules in English, it is not always adhered to.

The downvotes are nothing to do with me and this seems to be the real content of your last post, along with a large clutter about not giving a shit. Actually I find that using google is good for finding threads on subjects at SF. Put in SF plus subject plus any members you know have responded. The place for your resume of Cohen's book should surely be in this thread ? I have recommended some beginner's books on logic in other threads but don't know this one so I am interested to know more. You may like to look at E J Lemmon's "Beginning Logic" and Simmon's "Introduction to Topology and Modern Analysis" if you don't already know them. I have also found the book reviews section at SF to be pretty unpopular for some reason I don't understand.

Yes this is a profound statement and very important in calculus and analysis more generally. This was why I said that dx on its own is meaningless. Yes a limit has one numeric value, if the limit exists at all. But this x can never = 0 statement is not right as it stands. We will come to a proper version in due course. But first some background, that will become increasing useful as things progress. Note the author says that Analysis is mostly limis and calculus, but it also includes stuff about functions, sequences and series which are necessary to move on from the algebra of quadratic equations. So let us start with variables and functions. You will be please to hear that we don't need the whole apparatus - That can take a whole semester by itself - just some of the bare bones. So variables. A variable is perhaps the most self evident word in Mathematics. It really does exactly what is says on the tin and no more. A variable is something that, well varies. More precisely it may take on many different values. And a numeric variable is a variable whose value is numeric. Your x is a (usually) numeric variable. So what values can a variable have ? Good question, note I may take on, not does take on. The question is incredibly wide since all we know is that the value of our variable is a number. So any value between plus and minus infinity will do. Enter the mathematical function to the rescue. The main part of a function is a rule or equation or other expression for obtaining (numeric) values. Other parts limit the actual numbers we are allowed to use. So the square root function excludes all negative numbers. That still leaves a lot of numbers available. Since x is a variable, we can expect most functions of x to also be variables. We put different numbers in and expect to get correspondingly different numbers out. An exception to this is called the constant function. You get the same number out, whatever number you put in. OK numbers in ; numbers out. We now have two variables, x and f(x) and we can start going places. I have said f(x) since you have used it. But I am now going to change to y = f(x), which is using the rule to define the function as most folks do. So the next thing to understand is that x and y or f(x) are two different types of variable. x is an independent variable, which means that we can put in any number we are allowed. y = f(x) is called a / the dependent variable because its value depends upon the both the number we put into x and the rule which generates y. Having swallowed and digested all this guff we know enough about variables so are now ready to examine all the types of the 'd' in dx. 'd' is called an operator. An operator performs some process on the variable it operates on - in this case the variable x. This is the reason for changing from f(x) to y. We can operate on y with 'd' to get dy. We will tackle that next time, but a question of you if I may. Another person in another forum has asked a very similar question. Have you any relation to Idon'tknow, elsewhere ? I want not mix up answers to each.

Perhaps if you put some of that effort you are putting into promoting a logic forum into explaining about this book ?? Also have you looked at some past threads on logic here in the forums ?

Here are a few examples of what the silent e does. say tube now say tub say range now say rang say orange now say orang say voltage now say votag Does this help ?

Not sure about this as an example. The main thing is that a magnet is a source of force not energy. Force and energy are different things with different properties. In particular you can use up all the energy from a source of energy, but you can't use up all the force from a source of force. Note I said a magnet is not a source of energy. This does not mean a magnet has no energy, just that to use a magnet to obtain energy you require another party to actually do the work that becomes the energy you obtain. So if you hold a mgent in your hand and drag some nails etc along the table you are doing work (ie sufflying energy) not the magnet. The magnet is an intermediary that supplies the force instead of moving the nails direct with your hand (when you are still doing the work). But acid may contain considerable energy, but this will become exhausted with use, unlike the magnetic force exerted by a magnet.

I downloaded the third edition and I can't say I'm suprised you are confused if you are really using this book to learn the differential calculus. In particular my edition does not contain 'x' on page 7, 8 or 9. I asked you what you thought 'x' is because all those comments of yours that I have quoted suggest to me you don't understand this. It is vital that you do understand since 'x' is not a number. In arithmetic/algebra 'x' often stands for an unknown number that is to be determined In calculus 'x' is something else entirely and the book uses it in this way, but does not explicitly make this clear. 'x' is a variable. So that is where we should start. Do you wish to go on ?

That wasn't the question you asked. If you are serious about understanding please try to pose you question simply but completely and without mockery. They someone here may be able to help you. I have no idea what you mean by "x can never be 1" Can you give a complete example that confuses you? I suggest you start by saying what x is.

I doubt that many teachers would claim that Calculus is 'all about' anything. There are many calculi (the plural of calculus) and each has a different purpose. First there is the hint in the name 'calculus' = that which enables calculation. What you have described might be said as the introduction to what is known as 'the differential calculus'. This is indeed about change from one point to another. That point may be in time or place or connected to some other measurable quantity such as money or population or wheat yield or many other things. But there is so much more. There is 'the integral calculus', which is not about change but about summation. This is about what happens when you combine things together such as the energy you consume when you run 8 kilowatt shower for 30 minutes. Then there is the calculus of variations which is about minimising or maximising something. For instance what shaped curve will result in an object slding down it the fastest ie in the least possible time. This shape is known as a brachistochrone curve, if you want to look it up. MigL mentioned Newton - he allegedly solved this one is a day using calculus. Finally here is a very simple calculus, known as Russian Peasant Multiplication for calculating the product of two numbers. say 64 x 61 Write the two numbers down at the top of two adjacent columns Successively half the first column and double the second until 1 is reached in the halving clumn Strike out all pairs with even numbers in the first column Add those left in the doubled column thus 64 61 32 122 16 244 8 488 4 976 2 1952 1 3904 answer 64 x 61 = 3904 done without learning tables.

That doesn't make sense. Don't ask me, you wrote it and I merely quoted it. Well you haven't specified the issue properly and I'm not a mind reader so here is your answer. Just identify where on the chart your barrels fall. Interesting find. Thank you +1

I'm glad to hear the Boyle is not turning in his grave. In my book this was clear enough. Since volume = Area cross section x length reducing the length by a factor of 10 reduces the volume by a factor of 10. Boyle, rest his soul, requires that this increase the pressure by a factor of 10. Please read more carefully. I have, at no point stated the air would escape or be driven upwards, downwards or anywhere else. I simply asked you where it would go. Because the alternative is compression, whether for all or just some of it. The phenomenon that if you try to pour too much liquid down a throat or pipe then the air will push back is well known. It can be observed in bottles, laboratory glassware, peipes, and a myriad of other installations. The OP states quite clearly that there was too much water. This can't have occurred 24/7 every day of every week of every year. By psyclones seems to have abandoned this thread so I have no further information. I restate my conviction that at present we do not have enough information to properly determine the cause.

Has someone repealed Boyle's Law whilst I was out walking the Mendips today?

Obviously you are not listening to what I am saying so I will leave you with with this thought Say a 10 foot vertical pipe, initially filled with air, experiences a sudden influx of water that blocks upward venting and compresses the air to one foot. Then unless that air has somewhere to go it will now be at a pressure of 10 atmouspheres. Thus it will exert an upward force 10 times that of the atmousphere above the water. But by all means continue to fly in the face of established regulation and practice.

If there is anything else in the pipe at all (other than pipe of course), the water column cann be 'unbroken'. If you mean something else than please be properly specific. Please also give some consideration to the mechanisms I expanded on for you. They form part of the UK Building Regulations and I'm sure there will have been many BRE papers on the subject preceeding the embodiment in regualtion. Don't forget at the outset there is nothing but air in then pipe, not a column of water. Before the pipe can be filled with water, that air has to be dealt with.

That doesn't make sense. How can there be both an unbroken column of water and a (partial) vacuum in the same pipe?

Imagine a down pipe full of air. Now suddenly fill the top with a plug of water. Unless the air beneath the water goes somewhere, it must suffer increasing compression as the water falls. This in turn offers increasing upward force to the water, which is effectively saying a reduction in gravity, thereby slowing it down. So I asked the question; where does the air go ? Various methods are employed to vent or dispel that air. The siphon/suction effect occurs when a charge of water (and perhaps other material) drops down past a side junction. This can draw the air out of the side junction after the charge has passed. It can even be enough to empty the water traps in the side branch. Again various methods can be employed to obviate this. My guess is that the screw is meant to induce a swirl of vortex motion into the water to vent that air. This is similar to letting the water out of a bath where there is section at the centre of the vortex which has no water and the air beneath escapes upwards. When the bath is too full there is no upward vortex and the water empties more slowly. But I also guess that part of the fault lies in the roof/gutter profile creating this plug of water at the entry hopper during heavy rain, whihc was why I asked about it. @OldChemE might be a sufficient pipework specialist to comment here, he has probably met this phenomenon many times.

There is no siphon effect in this case; quite the reverse in fact. I was hoping my nudge would make you think about that.

More to the point, where does the air go ?

I see that this thread is still going. Since you asked a scientific question about Science you should expect a scientific answer. I gave you one just before you posted this, but you have not answered. It really is very simple if you don't keep introducing all sorts of inappropriate ideas. The free surface of a liquid in a container demonstrates the phenomenon of acceleration very simply.

An interesting topic. My guess would be that the problem had less to do with downpipe sizes and more to do with inappropriate roof/gutter profiles. It is necessary to develop a pressure head to force water through a pipe as you observe. This is known as the backwater curve and often forgotten in the hands of inexperienced designers. Some information of the roof/gutter profiles would be useful.

The plus sign in the formula refers to the arithmetical operation of addition. (and the negative sign in the other formula refers to the operation of subtraction). All quantities involved in that summation have a positive or negative sign as well. I say summation because the modern First Law includes other forms of energy as well So ΔU=Q+W + gravitational potential energy + electrical energy + ............+....... Each of these can be positve or negative quantites in their own right so imagine the confusion if you had to remember a formula where some where added and some subtracted. Since it is possible to have a a single sign convention which applies to all quantities, it is so much easier. Not all summations are so fortunate. Why on earth should Q and W not be either positive or negative. This was one of Joule's earliest experiments, to heat water with a mechanical paddle. Think carefully about this. Say you have an electric fire. You have electric energy in and heating effect out Now say you have an electric motor You have electric energy in and work out. Now say you have a dynamo You have work in and electric energy out Now say you have a steam turbine electric generator. You have heat in and electric energy out. Note the First Law is really a restricted form of the Law of Conservation of Energy and it is desirable for all forms to be set out the same. Another form is Bernoulli's equation in Fluid Mechanics which considers conservation of Gravitational enrgy + pressure enrgy + kinetic energy of the fluid.

Yes this confuses many people and is not the only situation in Science where sign conventions differ. Here we have the situation that the original Laws of Thermodynamics were written by folks who worked with steam engines. They put coal or wood into the machine and took mechanical work out. To derive the First Law break the process down into two stages, so there is an intermediate stage. First add the heat put in from the coal, then subtract the work performed by the machine. The machine must have had some internal energy to start with add to this the heat energy from combustion of the fuel and you get the intermediate total internal energy as a sum [math]{U_{{\mathop{\rm int}} ermediate}} = {U_0} + Q[/math] Then we get the machine to perform some work - that is we extract work. This must come from the internal energy, which is now increased to Uintermediate , [math]{U_{final}} = {U_{start}} + Q - W[/math] Which means that we subtract the work [math]\Delta U = {U_{final}} - {U_{start}} = Q - W[/math] Which is the form you will find today in most engineering and many Physics texts. But if you look carefully you will note that the heat added is input and the work extracted or output. When other scientists started to widen thes scope of these laws they wanted to consider all forms of energy, not just heat and work. Furthermore they wanted them all to be additive (that is you could put work in as well as take it out etc) So they adopted the sign convention that all forms of energy are considered positive in themselves, and it is the input or output that carries the sign. So input is positive and output is negative for all forms of energy. This leads to the form of the First Law used by Chemists [math]\Delta U = Q + W[/math] Where Qis the heat added to the system and W is the work done on the system, So if heat is generated by the system or work done by the system they are negative.

Agreed. Here is a slightly different point of view, especially since you mention chemical reactions. Acceleration is a second order measure of something which is already a function of time. In your case you are talking about velocity, which is a spatial function of time. (velocity is time rate of change of a line in space.) I think your difficulty comes because you are concentrating on the 'something' not the time rate of change. I know that all sound pompous but here is a chemical example that may help. In Chemistry we talk about the rate of a chemical reaction, meaning the time rate of change of the quantity or concentration of a reactant or product. We also talk about an accelerating ( or decelerating) rate of reaction as as the measured quantity builds up or reduces whilst the reaction is taking place. So in keeping with my definition, acceleration of the rate of a chemical reaction is the time rate of change of the time rate of increase in the quantity of product. Thus it is second order because the rate with respect to time is invoked twice.

Seems to me that an oxidation number of -4 is allocated to the carbon and +1 to each hydrogen halfway down page 422 of my attachment. I agree that some oddities occur, for instance when they lead to fractional oxidation numbers. For this reason IUPAC has withdrawn their use. However they are still used to bamboozle schoolboys. Oxidation numbers are a model of what is happening and like all models are limited in situations where they match what theya re modelling.

What do you understand an oxidation state of zero to mean ?