BigMoosie

This is true for any function, you could replace 'log' with 'sin' or 'exp' or anything else. See http://en.wikipedia.org/wiki/Distributivity

The eqality [math]2 + 2 = 4[/math] does require an assumption: * For every natural number n, Successor(n) is a natural number. See the wikipedia entry on Peano axioms. I agree, but I wouldn't say it doesn't contain any actual knowledge.

A negative charge is the opposite of a polar charge in the same way that a north magnetic pole is opposite to a south magnetic pole, we assign positive and negative as a way of show direction, that is all. I don't think it can be claimed that there is truly a negative quality there. Negative numbers are just as fictitous as 'imaginary numbers', they are an extrapolation of the tangible concept that is 'natural numbers' (ever wondered why they are called natural? they're the only ones found in nature). In my view any non-integeral number is a man made concept, even rationals. For instance how can you half of something? Half an apple is really 1 piece of an apple that has been broken into 2, the comparison '1/2' as a number is something humans devised, it is a comparison, not a number in the most natural sense. Of course this whole debate is just philosophy, the fact that water can be divided into atoms rather than being a continuous fluid affects this debate (something which should not affect mathematics in its purest sense).

I believe the derivative would be 1+i: f(z) = (1+i)z f'(z) = 1+i

Don't be biased; it could also be a very small value of 5, and bad interpretation.

Looka much better, but I still feel the avatars need 1 or 2 more pixels spacing from the frame. Cheers, -Moosie

Not many computers use that technique, only ones hooked up to special hardware, like a half silvered mirror + laser aparatus, mostly for scientific research. Most computers instead use the computer's internal clock to create Pseudo-random numbers. But then you would never get '1', if you want to cheat I would suppose this would be hard to notice: var count = random5(); function random7() { var r1 = random5(); var r2 = random5(); count++; return (r1+r2+count)%7 + 1; }

My thoughts on 'Avater on left': - The avatar needs more spacing, a few more pixels to be as spaced as when on the right - The vertical grey line is ugly, I don't think it should be there. If you want to seperate it visually from the text then a larger horizontal gap between the two would be better.

Ah right, I was so sure for some reason to the contrary. (sorry for not reading your earlier post correctly).

Isn't that a bit like saying: [math]\frac {65}{26} = \frac {5}{2}[/math] ...because you can remove the 6 from the numerator and denominator? (rather than divide both by 13) If you're going to use a technique that only works in some cases then you must justify why it works in this case. Merged post follows: Consecutive posts merged It cannot be any value, only 1 or 0. Try to find another value for a limit in the form of "0^0", it is not possible.

Thanks Martin, your response gave me the insight I was after. I didn't realise the big bang had little evidence, I always thought it was generally agreed upon. Also, it should have been clear to me that under a big bang situation it would have had to decellerate before accelerating, since the big bang would have had asymptopically infinite acceleration at the start. Regards, -Moosie

Your approach fails, you cannot break the exponential into separate parts and resolve them, a counter example of this approach would be: [math]\lim_{x\to 0}\; x^{(1/x)} = 0[/math] [math]\lim_{x\to 0}\; x = 0[/math] [math]\lim_{x\to 0}\; [x^{(1/x)}]^x = 1[/math] This is incorrect, in this case it is actually 0. The limit does not exist for [math]0^{-}[/math]. You cannot take a negative number to the an infitessimal power.

Although I used it as an example of a bad example, I partly agree. It seems we are trying to find a definition of Maths that is as rigorous as typical Mathematical definitions are. Perhaps the English language is not suitable for such a definition and we can just put up with "yeah maths is this sort of stuff" and move on? Perhaps maths is whatever an individual wants it to be?

I think there is an ideal solution where no random numbers are lost. It would involve running an algorithm which will produce a random number of random numbers in the range 0-6 (I'll start at zero to make the math nicer) and queue them up until when they are needed. In the algorithm random numbers (0-4) are iteratively added to a stack. Each time one is added, the following check is made: Let L be the length of the stack. Let X be the base 5 number representation of the stack, eg: a stack of [2,4,0,3] = 2*125 + 4*25 + 3. Is there a K such that [math]X < 7^K <= 5^L[/math] ? If so we can break this loop. Now let Y be the base 7 number representation of X. The digits of Y are our random numbers in the range of 0-6 that can be queued up for when needed (when they run out run this algorithm again). I'm quite sure the loop will use a finite but arbitrarily large number of iterations, but am not sure how to prove it. And of course, using an arbitrary number of iterations is fine since it also outputs a correspondingly large number of 0-6 range numbers, hence nothing wasted. In case it's hard to understand what I mean, my first post here would be what would happen on the second iteration.