studiot

This is where you need to be precise. You are asking if your set B contains more numbers than your set A. In order to approach this question you need to precisely define. What you mean by more than? Which in turn begs the question what do you mean by "How many numbers does either set have"? Edit Nice simple answer wtf.+1

Well I had no idea that English was not your first language, yours is very good. So perhaps that is why you misread my purpose? Nor do I have any idea of your level of knowledge in mathematics. All I have to go on is your use of words which (no offence) is imprecise. Precision is very important in mathematics and I would have thought you might be interested in knowing the correct words. I have put a lot of effort into avoiding the imprecise statements that are often made in answering questions about this subject. But I did make a start on answering your question, I just did not finish it since there is a lot to take in. So my question at the end was designed to find out if you had any problems with the necessary background. So I'm glad to hear that you have followed it all.

Infinitesimals are not numbers.

Please use the word set for your collection of numbers - this is the accepted correct term. Older names are aggregate or collection or sometimes class. A 'group' is a very important particular type of set in mathematics and only some collections (sets) of numbers form groups. OK so the set of whole numbers has nothing between each member of the set. However the set is 'open ended' (has no beginning or end) as we can always add or subtract another 1 from any proposed first or last number. We say that the set runs from negative infinity to positive infinity, although infinity itself is not a member of the set. That is infinity is not a whole number. We use the positive whole numbers for counting (posh math word - enumeration) things. In particular we can (try to) count the number of members of any given set. 1,2,3,4.. etc We use this 'count' to measure the size of a set and compare the size of one set with another. This works just fine for the number of members in a finite set. So the set {1,3,5,7} which has 4 members is bigger than the set {1.3.5} which has only 3. But we have already noted that there is no end to the process of adding 1 to the count. We never actually reach 'infinity' So the number of members in the set of positive whole numbers is not a positive whole number. It is in fact a (the first) transfinite number or 'infinity'. Another way of looking at counting is the idea that we are putting the members of the counted set into one-to-one correspondence with the positive whole numbers. 1 2 3 4 W X Y Z So in considering just the set of positive whole numbers we have found an infinity. But we haven't included any of the fractional numbers in between, let alone those that can't be expressed as fractions. So we are forced to the conclusion that more transfinite numbers are needed to place infinite sets into one-to-one correspondence. How are you doing so far?

Am still waiting for the aforementioned comestibles to emerge from the roast spud server, so Dave please adjust the third one. Here is a scream shot. Oh dear can't upload this one, error 500 received.

Both are right! The Biot-Savart page is simply more complete in that it takes into account the medium via [math]{\mu _r}[/math] For air and many purposes such as the space between sub atomic particles [math]{\mu _r}[/math] is so close to 1 that we often ignore it. That is what is done in your second link from hyperphysics. A more satisfactory way to deal with this is to use [math]\mu = {\mu _0}{\mu _r}[/math] Then there is no ambiguity. Incidentally your hyperphysics link has some good pictures of the circular magnetic field lines around straight conductors carrying current. Look carefully at these and think about your other thread on crossed wires.

Since you posted this whilst I was busy polishing my own post, please see the last version.

I don't see a correct question asked either. So I thought sensei's answer pretty imaginative and thoughtful. Since we don't know where A, B, C or D are or which way L1 or L2 are flowing, and our answer options don't include a no effect option, suck it and see is the only sensible answer.

Said it all, Sensei +1

We want our inner product to be a map from a vector space to the Real numbers ie a scalar. Consider any complex number a+ib (a + ib)2 = (a + ib) (a + ib) = a2 + 2iab - b2 Which is another complex number ie another vector. To get a real number we must multiply by the complex conjugate (a + ib) (a - ib) = a2 + iab - iab + b2 = a2 + b2 This will always be a positive number we can take the real square root of. Don't forget that vectors here are Euclidian vectors and the inner product represents the Euclidian norm with is defined as the square root of the sum of the products of the coordinates.

Since you clearly wish to simply mess about without making a serious proposition I bid you and your thread adieu.

Does something require embodiment to be real and part of reality? Consider this example. I pick up something and pull on it. It stretches some. Then I let go. It returns to its original size. I pull on it some more (a bit harder this time). It stretches further and again returns to original condition upon release. This is called elasticity. So does elasticity exist? It elasticity real? So Can I weigh it? Can I see it? Can I smell, taste, feel, etc it? Well actually none of these. Yet I maintain that elasticity is real and that any system of definition that is unable to cope with this simple example of abstract existence is seriously deficient. We deal with many far more subtle effects in our encounters with reality than this so we need a sophisticated definition to cope with with all the vagaries and ramifications.

You that you have not yet answered the question I asked several times in this thread, most recently in post#45. Can I remind you that it is an express rule in the Speculations section that you do this> So before rushing onwards, taking nobody with you, please pause and give me a satisfactory answer. What does this thread have to do with its title about Newtonian Physics?

Do you also consider phlogiston real, just because famous people for at least 1500 years proclaimed it so?

Some general font rules. 1) In the days before computer screens, much study was put into serif v sans serif fonts. The serifs were found be a marked aid to accuracy and speed of reading of block or body text, by humans. Special fonts for headlines were developed with different character aspect ratios and spacings for titles and headlines. It was found that sans serif lettering were better for short posters etc, although many fancy fonts were developed for artistic style and effect. 2) I was also found that sans serif fonts were more legible in cinematography, where again short pieces of text were projected. 3) This was repeated on computer screens and projected computer presentations with the likes of Powerpoint, Astound, Flash etc. 4) You also mention for science and maths. This presents additional challenges since some fonts make it difficult to distinguish the letters I and L and the numeral 1. This can be important where there is no regular flow of English due to the use of symbols. Italics are often used in papers and some fonts have special italic versions. And of course there is a whole panoply of special scientific symbols out there, not available in either standard serif or non serif.

I fully accept mine is a very basic and simplified introduction, but I'm not even sure that the OP has enough Chemistry to correctly count the carbon atoms in each compound. We did not cover the symbolism/convention as to what is at the ends of the 'sticks' or 'stalks' in each displayed formula in the last thread. So that will be the first hurdle to overcome. Whilst MAPP gas might be 'common or garden' in some circles, we have just finished explaining alkanes to the OP, so allenes? And do you count the nitrogen in the third example as a heteroatom? But I also accept you are much more knowledgeable here than I am, so please continue to butt in.

In your previous thread you told us that you are transitioning from High School to College. I don't see this as a question in this context, although that said the answer lies within the scope of the old fashioned UK A level. But you obviously need to know a bit about bonding. It is probably easier to count the carbon atoms in each molecule (you have to do this anyway for the comparison part of the question) then identify the atoms which are not sp3 hybrids and subtract. You do not need to try to work out each electronic configuration I said in your last thread that carbon is tetravalent. The sp3 hybrid is the ordinary common or garden single bond when all four bonds are identical (and therefore single) as in the methyl group I mentioned. So have a go and see if you can deduce the correct answers using this information and then post them here. We can take it from there and perhaps explore the meaning of sp3 hybridisation. Do you know what s and p orbitals are?

Thank you for your reply to my post #40. Unfortunately you still have not answered my question What does all this have to do with Newtonian Physics? If you are not talking about Newtonian Physics, why did you state explicitly that this is what this thread is about in the title? Can I recommend you study the English Dictionary, which contains Science, rather than the Secret Doctrine, which does not. Blavatsky at least got her English correct when trying to communicate with the Astral Plane. This is not being rude it is simply an expression that if you misuse common scientific English words you will not be understood.

I am travelling today so I will be able to generate some diagrams in the next few days after I return home. The more I think about it the more tricky it becomes to generate a good animation but I really like the idea. It seems important to decide what aspect of the wave is to be displayed since you have both time and space to play with.

Hi Mordred, sorry I can't cut and paste on this pesky pc so I refer to line 6 of your post#232 Your position points define a displacement, and these do not have to be 'real' in the sense used in the Principle of Virtual Displacements. In fact that is really the idea behind the calculus of variations. All non extremal displacements and actions are, in a sense, virtual. The other plus point for the POVD is that it works with both linear and non linear, Newtonian and non Newtonian mechanics.

Because my definition of reality follows English in including abstract nouns. It exists because we have invented it. It has, however, less merit than caloric which enjoys at least some use in thermodynamics, but can be equally falsified in other uses. The fictitious current in electric circuit theory has more use and is self consistent.

Please see my last edit. Yes the darker and lighter partly answer this but the diagram needs some accompanying explanation. I admit I did not notice the shading until you pointed it out, thank you. However my comment i8n pulsing still stands.

Measurements are good. Physicists should never be afraid of getting their hands dirty.

Perhaps everyone could cool off and stay on topic? Talking of topic I don't understand the title of this thread if you are not discussing Newtonian/Euclidian physics. By the way the fourth 'dimension' in 4d relativity space is not time but ict. Using time alone has the wrong units. And the square root of minus one has to be included to get the metric signs right.

Perhaps Physicists sometimes forget this as well? In order to mathematically guarantee the calculus of differential geometry on manifolds you have to restrict them to finite subsets of Rn, otherwise you cannot generate the necessary neigherbourhoods.