studiot

An embedding is technically an injection An injection is a mapping from a domain set to a co-domain set (they may be the same set or different sets) If every member of the domain is mapped to (injected) to a member of the co-domain and vice versa the mapping is said to be onto. This is the case when embedding an N dimensional object in an N dimensional coordinate system. If every member of the domain is mapped to a member of the co-domain, but not all the codomain members are used the mapping is said to be into. This is the case when an n dimensional object is embedded in an N dimensional coordinate system (n < N). So yes, though you would probably not bother with the distinction.

Excellent answer, Moontanman, +1 You have been doing your homework.

Or indeed an N dimensional object. I think you mean of dimension less than or equal to N. Physically, wouldn't a point be the smallest unit of space? Well according to Euclid a point occupies zero space (space = volume as Mordred likes to say)

Well there you have an immediate problem. Is -1 smaller than zero? Or is zero the smallest unit of some measured value? Of course in quantum theory the 'smallest unit' gives rise to the uncertainty.

I think that is a metaphysical point you are making. It certainly disagrees with Euclid. The first of the Fundamental Definitions, which precede event the axioms, is A point is that which hath no part. An old fashioned way of saying zero dimension. For those interested the second fundamental definition is A line is a breadthless length. Of course, the ancient Greeks disagreed on definitions Aristotle: A point, a line and a surface all define the prioor by means of the posterior, a point is an extremity of a line, a line is an extremeity of a surface and a surfeace an extremeity of a solid. Proclus gave us A monad having position. The modern view of a point is as the limit of some process.

Yoy said 30% HCl, but what you didn't say was what you meant by this 30% w/v or 30% w/w? The most likely meaning is the first one. I see that you have enough Chemistry to be able to calculate the required mass of HCl to react with 10g of carbonate. From this can you reverse engineer 30%w/v to accomodate this figure?

Welcome Oliver; What in the water do you think could become radioactive?

Welcome Ben; Is this classwork/homework? Part 1) If so can you tell me the reaction equation? Since you have used a fancy word (stoicheometry) can you calculate the molar masses of HCl and CaCO3? Do you know if the carbonate is monvalent, divalent or trivalent? part 2) Any Chemistry library or lab should have international tables where you can look up the density of hydrochloric acid at various concentrations. You can probably google this as well. This will be empirical, there is no general formula you can use.

This second quote was not addressed to me but seems to me to be the most coherent and cogent statement you have made here. It begins to address my question about your use of the term 'velocity', which I will reproduce yet again for your convenience. It also introduces some useful thoughts for comments to help you communicate since I am beginning to get an idea of what you are talking about. But please answer my question since I believe you are using some terms in an unconventional way and confusing many responders including myself. I have emboldened the original question but reproduced the quote where I added further explanation. The as measured velocity of a rocket ship (particle) whose velocity is approaching the magnitude, c, behaves differently from the as measured velocity of light. This is confirmed by physical observations. So please answer the question in the context of your hypothesis.

Intriguing thoughts. Welcome Razee. +1 How are you using the word "projections"? In projective geometry there are more points on the projective plane than on the Euclidian/Cartesian plane for instance. For comparison of planes the extra point is known as the point at infinity and is considered appended to the plane in question. Here are a couple of philosophical points to conside as well. You cannot have a 'point' without something that is 'not point' or 'no point'. So you need something additional to zero dimensions ie a null dimension to complete the set. This would be the 'point at infinity' in projective geometry.

What would you expect us to say? Congratulations you have derived the conventioanl formula for the area of a trapezium as being the average length of the parallel sides times the perpendicular distance between them. Incidentally I would check the first line of your proof for what I assume is a typographical error. BCEG is not a triangle as stated. Also the letters are not in cyclic order round the square.

That is an interesting conversation you are having with Strange, and to a lesser extent with swansont. What do they have that I don't, especially as your current conversation has a bearing on that question of mine you keep avoiding. Perhaps you only read the current page here and don't check if there were any replies since you last visited, but I spelled out the question yet again in the last post on the previous page. So please check back and answer the question.

Thank you, but That was not the Physics question I asked. I will repeat it since the question mark seems to have escaped you. The as measured velocity of a rocket ship (particle) whose velocity is approaching the magnitude, c, behaves differently from the as measured velocity of light. This is confirmed by physical observations. So please answer the question in the context of your hypothesis.

If you say so, I suppose it must be true and the discussion can proceed no further.

Well I did ask you a serious question about Physics. How about an answer? Thank your for the information, additional to your original posts in this thread. The point about the link between statmech and information theory is that they use they are analogs, in that they use the same mathematics (for somethings anyway). The difference is that information theory refers to something abstract (it could be the arrangement of marks on a pice of paper) whilst statmech refers to the arrangement of concrete things. (I am using abstract and concrete in their proper English language context here.) The commonality is in the mathematics of the arrangements, so it is not suprising (to me at least) that some of the results carry over. But what I am asking is do you know enough about the physical world to distinguish where they do and where they do not?

You need to make up your mind. Maxwell did not work in kg and metres. I gave you the modern answer because you posted a couple of paragraphs of working using modern units.

Considering you had to ask about magnetic poles along with your stated background, and I am still waiting for you to reply to my helpful answer to your question there, you seem to claim a great deal of knowledge of Physics. Considering the above, what do you mean by asserting the velocity of a neutrino is c? Do you mean the same thing that Relativity means in respect of light? Do you really understand these things? In particular do you understand the link between information entropy and statistical mechanics? Is it not because of this link that some of your equations come out the same as those of statmech?

Your lad needs also to start learning to 'read around' a subject as well as just lapping up the formal course material. I would avoid additional outside classes in the same curriculum as the school's. This will only demotivate him in class. Two fun books to help here could be Things to make and do in the Fourth Dimension By Matt Parker Mathematical Models Cundy and Rollett

The formula was originally due to Michell in 1750. The actual units have varied over time and there should be constants added depending upon the system of units you are working in. In modern MKS units the formula is [math]F = \frac{{{{\bar Q}_1}{{\bar Q}_2}}}{{4\pi {\mu _0}{r^2}}}[/math] where the pole strengths Qbar are measured in ampere-metres (amps times metres) Does this help?

I don't, it is one of the questions no one knows the answer to, although many have considered it over the millennia. But then, exactly the same can be said of a finite system. But I will wait for you to have time to respond properly to my last two posts instead of misreading them in haste.

I have already answered this more than once. The First Law does not apply to infinite systems, though relying on Wiki is dicy at best. Furthermore it is not known if the Universe is an isolated system. I find this too restrictive a condition on the definition of Science. For instance in many cases you have no way to test the actual happening of a historical event, but Science can investigate and provide probabilities of possible facts. A simple example would be the so called coffin ships.

Duplicate thread

I wonder if you are referring to where I offered a case in Mathematics of something which has a beginning, but no end? For instance the natural counting numbers. I was going to observe that there is another process in Mathematics whereby something is generated indefinitely, constantly expanding the something. For instance between every pair of real numbers there is another real number. The same is true of the rational numbers, but in that case there are also other non rational numbers between every pair. I thought you had given up responding to me, and as everyone else seems only to want to take the piss I had given up on the thread.

Forgive me but what's a micromole per minute per micromole? I've never heard of them.

Hello, KFs, and welcome to ScienceForums. You have done some good work and congratualtions on posting your attempt. So why not amaze yourself and finish the job? When x = 1 [math]\frac{{ - 4{x^3}}}{{\sqrt { - 4{x^4} + 13} }} = \frac{{ - 4}}{{\sqrt { - 4 + 13} }}[/math] Which you have already calculated.