studiot

Suggestions for using AI Combined with suitable human oversight, monitoring and controlling dangerous situations, places or activities such as prisons.

Surely you are looking at this all wrong because you should only allocate one axis per dimension. I'm sorry but although you quoted my previous technical comment, you made no response to it, instead taking the opportunity to promote another wall of woo. I have reported this for being placed in the wrong sub forum so I suggest you read the speculations special rules and contact a moderator if you need to.

What a pity you didn't simply ask how I came to my answer. If we try to substitute x = 0 into the given expression we find [math]\frac{{{2^x} - 1}}{x} \to \frac{{1 - 1}}{0} \to \frac{0}{0}[/math] Which we know we cannot do. But the situation is remedable as we can apply l'Hopital's rule thus [math]\frac{{\frac{d}{{dx}}\left( {{2^x} - 1} \right)}}{{\frac{d}{{dx}}\left( x \right)}} = \frac{{2^x}\ln 2}{1} = \ln 2 = 0.693[/math]

0 never 'equals '1 There are number systems without zero, it it not necessary for all number systems. From what you say you have obviously met some simplified explanation of the development of numbers and let your imagination run riot. The proper development of numbers is a very important and interesting (to some) subject in maths. We can discuss this properly if you like. I'm sorry but the rest of your post is just a kind of numerology, it is not science. Furthermore your 'stability' values fly in the face of direct observation. You should look at the 'packing fraction curve' ; Iron is the most stable element.

If you have your phone or tablet in a protective case, additional to the tablet itself, does anyone know or have any data on how safe it is to leave the device in the case for charging or should it always be removed ?

Thanks. Yes I have often collected quotes from various back pages by methodically going through and adding them to the imput box. Then moving on to another page and immediately clicking in the now empty input box at the bottom of the page which restores my previous collection so I can add to it.

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.