Dr Finlay

I like the explanation of a limit. One of those golden examples i won't forget, which is useful.

As far as i understand a limit, for example [math]\lim_{x \rightarrow 2}f(x) = 5[/math] means that if you take sufficiently large values close to 2, f(x) approaches 5. This could be thought of graphically. Imagine a straight line through the origin in the positive direction, as you increase the value of x closer to 2, the value on the y axis becomes closer to 5. There are many websites and tutorials which explain limits which i'm sure would be unearthed by a quick google search.

The road to reality by Roger Penrose is stuffed full of equations. There may or may not be something about superstring theory in there. It's probably worth a read though anyway.

Hmm, i think i may have worked it out. I drew a Venn diagram and got [math]P(A \cap B) = P(B) - P(A \cap B)[/math] so it follows [math]P(A \cap B') = P(A) - P(A \cap B)[/math] i then get the book's answers. I think i just needed to spend the time to work it out, cheers anyway.

Just done another question, i get a different answer from the book though. If A and B are two events and P(A) = 0.6 and P(B) = 0.3 and P(AuB) = 0.8 find:- a) P(AnB) b)P(A'nB) c)P(AnB') For part a) i got 0.1 using the addition rule, which the book says is correct. But for part b) i did P(A'nB) = (1 - P(A))xP(B) = 0.4 x 0.3 = 0.12 the book however says the answer is 0.2. For part c) i did: P(AnB') = P(A) x (1 - P(B)) = 0.6 x 0.7 = 0.42 the book gives the answer 0.5 Can anyone see what I'm doing wrong? Thanks alot, Rob

I got 5*, no age though. 5 stars sounds good though;)

I managed to get that far, but here's an example of a question. If S and T are two events and P(T) = 0.4 and P(SnT) = 0.15 and P(S' n T') = 0.5, find: a) P(S n T') b) P(S) c) P(S u T) d) P(S' n T) e) P(S' u T') All these questions should be able to be solved using the addition rule. But I can't figure out how to get probabilities of events not occurring from events that do occur, such as a), d) and e).

I'm Rob, from Yorkshire, UK. I'm studying A-levels having just started year 12 doing Physics, Maths, Further maths and History, currently trying to teach myself calculus from Stewart's book. As for interesting facts, i very nearly once met the Queen, and i have a fiver in my right pocket, which also oddly enough, sports an image of the Queen:eek:

You could try and prove riemann and scoop the big prize.

I decided to go over the probability section in my S1 statistics book. However, it seems i've stumbled at the first hurdle. The first exercise is about the addition rule P(AUB) = P(A) + P(B) - P(AnB). There is a question where it asks about the probabilities events not happening, P(A'), P(A'UB), P(A'nB') etc. I know that P(A') = 1 - P(A), but i'm completely stuck on how to get such probabilities of P(A'nB). Can anyone help unclog my mental block? Thanks once again, Rob

Thanks i'll have a look. I understand any number can be made into any other arbitrary number. I was just wondering if there was a way to derive pi from phi or phi from pi. I just thought there must be a way since these 2 numbers have unusual properties. All in all it was just a conversation at school so i wasnt expecting anything. Anyway it's filled in my "learn something new everyday" quota for the week.

Cheers everyone;)

Ah right. Cheers mate. As i said, i didnt think there was anything special about the way my equation approximates pi, there are probably an infinite number of ways. I was just wondering if there was an elegant way to connect phi and pi. Maybe i should have just said that at the start:embarass:

Could you rearrange [math] \phi^{(\displaystyle\frac{\pi + \phi}{2})}= \pi [/math] for [math]\phi[/math]? Are there any other ways which relate phi and pi, my method is rather poor, and only approximates pi to a few decimal places.