Since there are quite a bunch of nice people on this server who helped me out ingame, I thought I'd give back by starting a math thread. I'm currently working on getting my masters degree in mathematics, so... If you need any help with math-related stuff, feel free to ask a question here. I can help understanding stuff, give hints, etc.... (NB: I won't do your homework for you )
Math, High-School level: Look at this interesting way to use this function on this Graphical Calculator! We're geniuses! We know everything about this, we must be math wonders! Maths degree, here we come! Math, College/University level: Wait, wth? That doesn't make sense... and that button doesn't even exist! 200 calculations to get that? But I thought that would be easy? Ah, I think I got the answer... Wait, the answer is 3 root 2.5? Then I assume Pi (-6.23 x 10^7) is wrong...
I'm doing related rates and optimization in calc now, Its just a lot of derivatives, L'Hospiral's rule, chain rule, and product and difference quotients. Lots of stuff to remember
Oh, I actually remembered something: There is a very simple little thesis that one of the teachers I had, back in Japan, about 1 being equal to 0.999999... Then, when I came back to The Netherlands, one of my other teachers there discredited that theory, but never told me why... I wanna know which one is right, and more importantly, -why-... Thesis: Lets say, 0.99999... is now equal to x. This would mean that 10x = 9.9999999... Now, if we subtract x from 10x, you get 9x (logically) But, with the value being so, it is equal as to subtracting 0.99999... from 9.9999... which is 9. Then, this concludes that 9x = 9, and so x = 1. So 1 = 0.9999999... (I am sorry if this is a dumb question, but I, unlike you, never mastered in maths/logic, and walked the roads of science...)
Well, if you round of 0.9999 it comes down to one. :/ and I think that thesis might only apply to irrational numbers, which may be the reason your teacher in The Netherlands discredited it, as you could not apply it to rational numbers.
Tech, that's not true. Style's reasoning applies on all (real) numbers I have no idea why that Dutch teacher would say 0.9999.... is not equal to one, because it is (BSP's argument is one more rigorous way of proving it). I sure hope he's not your math teacher Another way to look at it is to realize that real numbers can have multiple decimal representations. Meaning, for any real number x, I could 'write it down' in different, although equivalent, ways.
well 1/3 = .333(repeating) 2/3 = .666 (repeating) 3/3 = .999(repeating) 3/3 = 1/1 = 1 Therefore .999(repeating) = 1
Same can be said with 1/9 and such (which my method is based upon), but I generally do not use that method, since "1/3" is 1 divided by 3, and if you divide something in an amount of parts, and then multiply those parts by the same amount, doesn't it become whole again? (Which creates a good question about philosophy, "We are merely the sum of our parts"... The sum the parts are 0.9999... so what is the final piece?)
