studiot

I must say you seem to have a very deep interest in this subject, far greater than my own, as you keep referring to people and things I have never heard of. If you don't like it, why bother ?

Your reply may be relevant to many things, especially since they are interlinked. However I am sorry to say that I still am no wiser as to what you are saying. Pewrhaps it would help if I observed (as I have dome several times in the past) that there is nothing you can say in Mathematics that cannot be said in plain English, the converse is not true since there are many things you can say (express) in English that cannot be said mathematically. Is this what you are alluding to ?

test test test Many thanks for your concern. As you can see from my test it is working now. I think I will blame it all on Dave - he was, after all , lurking about the time it happened. 🙂

OK This is useful. Yes f is a function. That is it is a whole set of values of y each one corresponding to a value of x. Important features of functions are. Each value of x must correspond to one and only one value of y However many different values of x may correspond to the same value of y For instance the constant function y = 3 makes y to be 3 for each and every value of x. The whole function is the whole set of pairs of values, one x and one y in each. y = f(x) refers to all the pairs (x, y) and may represent a geometric curve. If the function is not to broken up it may be 'differentiable'. This means a second function called the derived function or just the derivative may be obtained from it by a process called differentiation. Thus the derivative is a function, just like its progenitor. The integral on the other hand is quite different. To integrate means to perform some sort of sum. Indeed the symbol is a stylised Gothic S. When you perform a sum you add things up and come up with a number. A single number. Luckily there are some formulae for performing this sum, but as Genady has already said, there is no general formule. The Fundamental Theorem of Calculus also comes to our rescue when we want to find these sums ( hence the link to area, volume and many other things) I called f' the 'primitive' which gives rise to the derived function - You can also use the term 'antiderivative' if you wish. This is really wonderful news because it tells us that the number we want - the sum the integral represents - is the difference between two numbers, the value of the primitive at each end on the region. I say region because the simple formula integrates (sums) along a line but the region may be a line an area a volume or more. A further comment looking ahead. Finding the primitive allows us to 'solve' differential equations which are equations containing both algebraic functions and derivatives. such equations arise quite naturally in just about every corner of science and engineering.

Exactly what I would expect your elementary Dummies book to say. So can you explain it further, what do you think f is? What do you think an integral actually is, when you say 'you are finding the (definite) integral....' ? What are you expecting to find ? These are not trick questions, they are meant to help you understand when I explain more fully. This explanation will include the reason I am putting the word definite in brackets. By the way the (definite) integral is not necessarily an area, though it can give you various area with suitable processing. For example the (definite) integral of sin x from 0 to 2pi is zero so it will give you nothing at all.

Well thanks for that. It is certainly non functional for me atm. All I did was test some Tex in the sandbox. Gosh that lot came up when I came to type in a reply, after entering your quote into the box. Weird. Anyway I would be very grateful if you could point me at any Firefox settings I can look at in W10

Consider the following Let [math]y=\frac{{{2^x}-1}}{x} [/math] What is y when x = 0 ? Clue it is not 1 it is about 0.693

[math]\int_a^b {df=f(b) - f(a)} [/math] Can you say what this means to you please ? It is known as 'The Fundamental Theoem of Calculus'.

In the past when I wanted to test or check something something during composing a reply a reply I could leave that thread make my check and then return to the original thread. So long as I simply clicked in the reply box before I did anything else, my previous typing reappeared and I could carry on. Why does this useful feature no longer work ?

[math]\int_a^b {df=f(b) - f(a)} [/math]

It would be helpful if you indicated what you mean by 'solve an integral'. I suspect you are looking for what is known as 'the primitive' in what is known as the fundamental theorem of calculus.

what an excellent reference. Also useful on the existence thread and good to quote to others about scientific method. +1 One thing I couldn't find in it was the companion, balancing quote

This thread is to open a discussion about this quote, its meaning and implications.

In my secondary school, there were two girls who could easily beat me at running (did I mention they both ran mid distance for England) and also one lad who could swim to the other end of the pool faster than I could get across it. (did I mention that he also swam for Emgland) Did that bother me ? Not in the least, though I did my best to beat them. Would it have made any difference if their genders were any different? I doubt it. Were there other pupils intermediate between myself and them? Yes of course. but I also represented the school in those sports.

So I'm as entitled to my view of 'fair' as Zapatos is entitled to his.

I don't see that the OP introduced fairness at all. So any suggestion concerning the current level of fairness is moot.

I am not interested in your age, but since you clearly think you know more than the experts here, I can only suggest you get a good book on NMR (Nuclear Magnetic Resonance) and the vibrational modes due to quantum angular momentum. Bu I have to tell you that you will find that rotational quantum mechanics has nothing to do with string theory, which has already been long discredited, as you have already been advised.

How is that what Richard asked ? ie how is the the probability P(y=g), which is the given question ? Edit Yes I see what you are saying now. +1

I think the question is ill posed. P(anything) is positive or zero. But the conditions given could include y(x) < 0 for all or some x.

Good idea. Most of Chemistry is to do with electrons in one way or another. It was once said that if you rubbed yourself with pig fat and chicken excrement it would cure syphillis. That was untrue then as it is now. Studying atomic vibrations is good, very good. How much do you know about vibrations ? Do you know, for instance, the difference between a wave and a vibration ? Talking of vibrations, I asked a few useful questions in a previous post. Are you going to answer them ? They were designed to be helpful.

Is it 'fair' that taller sportsmen and women generally make better fast bowlers and tennis players ? Is it fair that my eyesight has never been good enough for me to excell at my favourite sport ? Life is full of unfairness and inequity. Yet we have to somehow reach conclusions or results. They are rarely 'fair' as a result.

Here is some more meat, following on from my previous answer to your question. Modern teaching of set theory is generally oblivious to the deeper issues that occupied the minds of those around at the time of Russell such as the effect on the properties of the sets v the properties of the elements. Here is and interesting extract from a postgraduate textbook of the time which does not mention intersectioction, union and so forth whcih are the current foundations but spends several chapters exploring the above issue.

'Fairly'. Therin lies the whole intractable, squaring the circle problem. YOU (whoever makes the decision) has to be unfair to someone. YOU has to make a decision on something that cannot be completely resolved. Note I support neither side here and am sorry to read today's news about Lineham, whose antics I definitely don't support.

To put my figures in perspective say you had a picture of a string on an A4 sheet of paper. Then to put a picture of an atom on a piece of paper at the same scale you would need a piece of paper to be 0.3 x 1025 metres. 1 light year is approximately 1016 metres so your paper would need to be 3 x 108 light years or 300,000,000 light years This is the distance to 'nearby' clusters of galaxies, not stars or even individual galaxies. https://en.wikipedia.org/wiki/Coma_Cluster

Hello, Grayson. Are you sure you mean string theory not something else ? Your goal seems more about some form of quantum theory. Are you aware of the size difference between atoms (of the order of 10-10) metres and strings (of the order of 10-35) metres ? This makes atoms 10,000,000,000,000,000,000,000,000 times larger than strings so you would not really see strings on pictures of atoms. By the way, I see you are just starting calculus, trigonometry and chemistry and you have posted this in applied chemistry so do you understand this mathematical notation ? Just ask, we can help with.