studiot

What are you not convinced about? If you are not convinced, why did you quote these articles? I agree the Wiki article contains some glaring inconsistencies. Edit I have just seen this You asked this in another thread So here is a simple proof that there is only one null (empty) set. By definition two sets are equal if both sets have exactly the same elements. (Note in the context of sets this equality is an identity which means that they are the same) But all the elements of all null sets must be the same So all null sets are the same Or there is only one null set. Does this help?

What would happen if you interchanged the words set and category? One of my beefs with the system is that different, well respected, authorities use different words for 'category'. Russell developed a system of 'types' Graves, Simmons and Phillips use Classes Hobson and Kestleman use aggregate. Some (eg Borowski and Borwein) have categories as particular restrictions of classes, more general than sets, but less so than classes It is small wonder that outsiders of this clique are confused. The rest of your post simple demonstrates my point that there is a heirachy of different types of collected objects for different purposes, because some purposes are incompatiable with each other. For instance if we want to include the set of all sets or even a set which can include other sets we have to abandon a very important property of some sets. Namely that every member of the set is the same type of object and that defined operations on a set will apply to every member and always be guaranteed to be the only way to produce another member of the set and to always produce one. this is particularly desirable in numbers and arithmetic. Another oft required property is that each instance of a member is counted only once. But that cannot be resolve Russell's sock paradox. Sorcerer, I am trying to offer you a practical man's balanced view to make sense of all the confusion. I don't think you can start with some glorious fundamental set or collection and refine it to suit all purposes because of the incompatabilities. You need to start with what you want your collection to do for you.

In that case your subsequent remaks are not founded on any justification. To quote your later comment I'm sorry I didn't phrase it in such a way that you could understand it. ZFC theory is a restriction of a more general theory for a specific purpose (which I loosely associated with numbers). You say that ZFC does not define sets and said (or implied) last time that ZFC also does not define numbers. So why is the first OK but the second verboten? Finally in my study of Euclid, Definition 1 concerned a point, definition 2 concerned a line. Euclid puts the definitions where they belong, preceding the axioms which tell us what we can and can't do with the material of the definitions.

So you too have sidestepped the thorny issue of "What is a set ?". You use the word collection, I have seen the words aggregate, type, class, amongst others to park the problem one stage up-the-line. The problem is that no-one has yet come up with a definition of sets that is fit for all purposes we desire to use the concept for. So we have a 'bunch' of 'thingies' and restrict these to particular cases with particular properties, that serve our purpose of the moment, not caring that some excluded thingies break our rules. In fact we are so enamoured of this ruse that we construct a whole heirarchy of bunches and sub-bunches, each with a new name and more restricted properties. But hey, it is a good ruse and serves us well. How do you get on with Russell's shoes and socks paradox?

Whatever definition is offered for a set it will not satisfy everyone for every purpose. Various devices have been used to get around this difficulty. These devices usually amount to a restriction on what the theory under discussion applies to. For instance we can avoid the issue in the quote by simply saying at the outset that we are dealing with sets of numbers.

It is you that does not understand resonance. The soundbox in a violin is a resonant structure and the pulling into synchronisation of multiple oscillators is a resonance phenomenon. You example is an example of forced not resonant oscillation.

I note the initials AI could stand for a poster in this thread or somthing else in computer circles. I also note that AI claims to work for M$. In response to the hijack of my thread to advertise W10, please comment on this editorial in the current trade press.

The trouble with those pesky scienceforum members. They don't know when they have been terminated. They just keep getting up on going on. The world ended yesterdaaaaaaaaaaaaay.

The first thing to know is that there are two types of CRT and to find out which you will be using. Both types generate a beam of electrons emitted by the cathode and accelerated and through the anode. On passing through they impact on the phosphor of the screen whence light is emitted. To prevent build up the screen has an earthing layer. This electron beam constitutes an electric current. It is this electric current that needs to 'thread' any conducting pickup loop to generate current, and yes, if it does so it will generate current in accordance with Faradays's's laws. So much for the similarity of the types of CRT. Now for the differences. The electron beam is not arandom broad brush spray, it is focused into a tight beam that strikes as small a spot on the screen as possible. This strike spot is moved about on the screen to create the wanted image. The difference lies in the way the beam is focused and moved about (deflected). Two methods are available, magnetic and electrostatic. Magnetic methods are used in CRTs designed for television and computer screens. Such screens are designed to display what is known as a raster. In a raster the beam is scanned in regular lines abckwards and forwards across the screen, covering the screen in a series of lines. Electrostatic methods are used in CRTs designed for oscilloscopes, radar and echo sounders and similar instruments. The beam here is used as an electronic pen and 'writes' (traces out) a continuous line on the screen of the desired image, going where is will (needs to) in order to achieve this. Two comments about safety need also to be made. CRT's employ the use of (very) high voltages which can result in serious accidents if not properly treated CRT action generates x rays which can be a hazard if allowed to spread into the surroundings. Does this help?

One last time. No it doesn't. Read it properly.

Well I'm sorry if I drew the wrong conclusion there. I did find who said what to whom a mystery and I hope my comments were suitably discreet.

Let us get this out of the way first shall we? Here is the text of the last PM in my sent box sent, dated 27 January 2016. It had nothing to do this thread or you. Enough said? As to my statements in post#31 here I stated you made a false statement. Here it is This was made in response to my showing the GCSE classification into four layers where they classify the top layer as 'mainly charged particles' Yet you are adament that this layer has the same composition as the others. Note that the scientific and educational authorities include all the parts of the atmosphere I included and you consistentlywished to exclude. I think they are right and you are wrong, hence my contention of the false statement. Although my quote above was dislexic in the placement of the word large (which should have been largely) it does not alter the fact that I drew attention to a known variation of composition of some lesser components of the atmosphere with height. I have also consistently agreed that the main two components do not vary with height within this zone, which is the zone you wish to claim as 'the atmosphere' Hence my contention about you ignoring facts. Edit this section added later and meant as a separate post. Thank you Sensei for clearing up the PM mystery +1 I think perherhaps it may be a language issue but saying John made a false statement doesn't necessarily mean calling him a liar in English. That would be a much stronger statement which would be totally unwarranted. I think he just got carried away, as we say. I also didn't yet take the opportunity to thank you for trying to cool things early with your delightful videos, though I did give +1 at the time.

I really think this has nothing to do with you, Strange. But if you find the truth uncomfortable, fire away.

And why are you selectively ignoring or making false statements about valid statements that are made? That is not only bad science it is bad for science.

I said no such thing. Here is a quote from a GCSE (junior high school) revision site. Note they divide the part of the atmosphere you refer to into four layers. Stratification is still a rose by any other name. Note also that although they don't large discuss variation of composition with altitude their diagram clearly indicates that it varies since they show a water ceiling and a natural ozone layer. The atmosphere Layers in the atmosphere The atmosphere is the layer of gas around the Earth. The atmosphere can be divided into four parts: Troposphere: Where we live. Stratosphere: Some jet aircraft. Mesosphere: Space shuttle orbits within. Ionosphere: Mainly charged particles.

Quick reply, I will return again after I have digested your additions. Yes Fourier and his law of heat transfer is one two names I had in mind. Newton's law of cooling was the other. Standard heat transfer calculations are based on these. However you need to be careful if this is a building calculation because there are standardised approximations and assumptions made for the simplification of the calcs so they do not have to be worked from first principles every time. For building control purposes these standardised methos superceed first principle calcs. You mentioned the complexity of some maths you have found. Solutions to the equations have two aspects. Steady state and transient. The transient solutions are much more complicated and these may be what you have found. However Fourier's law does admit trigonometric series solutions for both cases. Edit add the following material Here is a good discussion of the maths. https://www.thermalfluidscentral.org/encyclopedia/index.php/One-dimensional_transient_heat_conduction_in_semi-infinite_body The first part of the article gives the basic time independent equations. The part you will be interested in starts at equation 23 where a periodic heating function, as you seem to indicate, is introduced. The analystical solution is then presented followed by a neumerical solution from equation 44 on. Note that in the numerical soltion an approximating function is used (they used a cubic, equation 50).

Sorry Fred, but you just mentioned the atmosphere, which does have layers as I described. JC refers only to the lower atmosphere which has such an overwhelming concentration of oxygen and nitrogen that any variation of other gasses (eg carbon dioxide is about 0.03 %) tends to get lost in the big figures. The other layers form the upper atmosphere and carbon dioxide does not extend this far so its presence largely concentrated in the lower atmosphere band.

OK so You disagree with this national document (in declaring my points irrelevent). http://www.nhbc.co.uk/NHBCPublications/LiteratureLibrary/Technical/filedownload,29440,en.pdf which says that carbon dioxide pools in depressions and methane collects under soffits, ceilings and other spaces confined by horizontal building elements. The document has extensive bibliography at the end to national research and controlling documents. There is also lots of other useful info about the gases. I wish I had this when participating in the design and construction of the Priory Fields commercial and the Salmon Parade residential developments in the 1980s. You are entitled to your opinion and I am entitled to mine without vitriol.

Hello Thomson and welcome. Please note that homework/coursework belongs in the homework section. It is also wise to allow sufficient time to gather responses on a science website, one day is not enough. Finally you need to post the actual question (don't worry about the greek letters we can help with that plus some idea of your thoughts about the question. Yes you need to derive a differential equation with respect to time for the heat flux. What physical laws or theorems do you know in relation to heat transfer? Hint they are associated with names of two of the giants of applied maths.

Strange, I have added +1 since I take it in good spirit, not as in any way disrespectful for those three souls who died in that hole (which I think was in Kent by the way)

Since I have no intention of turning this into an unseemly schoolyard slanging match I am going to make brief comments of the last couple of posts then present my own alternative view, which does not accord. Fred can then choose his own. interpretation. Thank you , John for all that working off of the Sunday roast. I don't doubt you figures except for one thing. You clearly misunderstood my example about the hole in the ground. I said, and I meant, that the Earth's atmosphere ie stratified. And that that statification is due to the varying pull of gravity on molecules of diffeent molecular weight. I should have added there is a second mechanism at work so will detail this in a moment. Stratified not continuously graded. Stratified means 'divided into (horizontal) layers of different composition. I am taking the atmosphere as being that body of gas that has a gravitational attachment to the Earth. So my information is that the layers are as follows. Up to 72 miles the composition is basically a mix of nitrogen molecules and oxygen molecules with 'traces' of other gasses. Since the molecular weight of nitrogen and oxygen is almost the same, and as John says, the molecules are moving pretty fast, there is no further stratification and negligable gradation within this layer. The composition changes above this height as the oxygen molecules and to a lesser extent the nitrogen dissociate. At about 600 miles the composition changes again the principle gas now being helium At about 1500 miles the composition changes again and this is where you will find most of the hydrogen in the atmosphere. Gasses beyond 21,000 miles have an average speed in excess of escape velocity so that is my upper limit of the atmosphere. So my stratifiaction occupies 5 distinct layers for the whole atmosphere. Now note layer 5 in particular. Mostly hydrogen. To bring this back to the Earth's surface and what I said about 'lighter' molecules consider the following thougth experiment. Line up some moderately tall jars of gas with lids. The jars contain carbon dioxide, nitrogen, methane, hydrogen. What will happen when I remove the lids? Why do you think gas detectors in buildings are mounted on the ceiling not the floor? I think the hydrogen leaves the jars immediately and heads skywards. The methane also migrates quickly upwards (hence my question about gas detectors). The nitrogen jar will take perhaps one hour to exhange enough molecules to have the same nitrogen/oxygen ration as the surrounding air The carbon dioxide will remain in the jar and still be in greater concentration than normal on the following day.

How does that address my post 34?

The multidimensional equivalent of the derivative is called the Jacobian and usually appears in Matrix form. https://en.wikipedia.org/wiki/Jacobian_matrix_and_determinant

This is difficult to answer since I don't know where you are, what your interest in electronic/electric circuits or what you have access to. Most of the books I would recommend are British, simply because most of my library is from British publishers, though I have some good American ones as well. First to distinguish between electric circuits and electronic circuits. The main applications of electricity are power (which includes domestic drills, heaters etc) and information/communications. Electric circuits are more geared towards power engineering and most books with this title may or may not have a chapter or two on electronics. Conversely Electronic circuits tell you about , well electronic circuits, have scanty basic information about power applications. Both are intensely practical subjects so the next question is what do you want this for? If you are following a recognised course towards professional application then you will need much more theoretical detail. If this is an amateur interest then a more practical approach that offers the right amount of the right theory would suffice better. For an amateur and even professional introduction to electronics with a wide ranging coverage the books by Michel Tooley and his Brother are brillaint. They offer a great deal of the type of 'why are we doing this' explanation I put into my posts above. 'Electronic Circuits' was one of the originals but there have been several new ones and revisions. http://www.amazon.co.uk/Electronic-Circuits-Fundamentals-Applications/dp/0750669233 Two other good books in the professional + amateur category are A Practical Introduction to Electronic Circuits Martin Hartley Jones Electronics and Electronics Systems George H Olsen Before you pay for the oft recommended american 'The Art of Electronics' by Horowitz Get it from the library and check it out. I cannot recommend it. A brilliant american book is Microprocessors and digital systems Douglas V Hall A good modern electrical circuits first serious book is Electrical Circuit Analysis and Design Noel M Morris Finally try this site, they were a really good bunch before they were taken over by a commercial enterprise, so beware the advertising, but they have the internet rights to the famous e-textbook by Tony Kuphaldt. allaboutcircuits.com Also beware the original Kuphaldt book uses the 1990 fashion of electron flow as the positive direction for current flow which can cause confusion. This is not a good idea and but was fashionable in the 1990s. In fact always check the work of any author anywhere before reading as to whether he uses what is known as conventional current (postive in the direction positive to negative) or electron current (positive in the negative to positive direction) Post again if you need more.