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.

I was not thinking simplicity, just computational efficiency, which yours of course improves upon. If the bottleneck of the original random number generator is a heavy bottleneck (eg. using an external generator), then I would probably try to devise some system where 50 random numbers are generated and something like ~35 numbers 1-7 are extracted from the results (can't be bothered figuring out exactly how many) and stored in a stack for later use, the larger the stack the fewer the random numbers will need to be discarded.

@coke: Your examples don't help your case since you didn't define any of them well at all. Really, try to provide a definition for Physics or Chemistry that people would be happy with if a thread similar to this one were constructed for such a debate on those topics. Chemistry is many things, chemical interactions are just one part of it. This is just as bad as saying: What is Math? Study of numbers, functions, etc. etc. The study of English includes much more than the language itself, it also includes (but not limited to) its usage, both historical and in various mediums (though I will contend that literature may be easier to define than Physics, Chemistry or Maths).

I like your response Sisyphus, in every way possible. .... Even the weird ways.

I agree with D H. In my view, math is simply: The persuit of any logic that is flawless under its assumptions. I hear you cry "But there's lots of controversy in math, how can it be flawless?", well controversy arrives in the bridging between that logic and the real world, for instance: * which axioms are chosen to align the logic with reality * controversy surrounding the introduction of imaginary numbers was based on the fact that it "makes no sense in reality", not that it isn't self consistent (and if people claimed it wasn't self consistant then that's all part of the "persuit") * controversy over machine proofs: under the assumption that proven machine instructions that provide results are valid, then whatever the results happen to be are self contained under that assumption, therefore it is maths. The problem occurs in the real world argument over whether that assumption is suitable for reality. Under my view, some philisophical arguments can be considered math which I agree with, if you don't agree those sorts of arguments are math then you will need to expand upon my definition or reject it (I'd be interested in arguments to either). Merged post follows: Consecutive posts merged I don't think so. For one, we are not discussing its use, it's clear what it is used for (whatever "it" is). And also there are many people (not just religious people) who reject definitions of branches of science, including the scientific method, evolution as fact, the importance of double blind experiments etc.

We know that the universe is expanding and the expansion is accelerating, it is also commonly believed that it has been acellerating since a universal singularity existed (the big bang). Assume that instead of the universe having always expanded but it goes through phases of acelleration and contraction akin to a sine function, that would place the current universe somewhere after a trough approaching an inflexion. In this question it does not matter what would cause such an oscillation, but I am curious about what observations contradict such an idea?

Your question is not specific enough as there are an infinite number of ways this can be done. Here is the first that comes to mind: Run the 1st generator twice, if you get: 1,1 -> return 1 1,2 -> return 2 1,3 -> return 3 1,4 -> return 4 1,5 -> return 5 2,1 -> return 6 2,2 -> return 7 else -> try again Each of these has equal probability, though it may take several iterations before it ends. Efficiency was not a requirement you provided.

I'm sorry, but I'm here to help with math problems, not software ones. Try searching the net for "spreadsheet loan payment", your problem is not unique at all. If you're still spreadsheet illiterate perhaps someone else will help you.

If you are using a spreadsheet you don't even need this formula, just prepare your columns for outstanding principal, etc. and use "goal seek" to adjust your principal to make the outstanding principal be 0 at some designated time. If you don't know what "goal seek" is I think you may very well find that it solves your problems. I don't know "Err:522" means.

Yes, X is the amount of the payment. Yes, Y.F means "Y multiplied" by F. There's one extra thing, I assumed that your installments are more frequent or equal to the compounding rate, if it compounds more frequently than you plan to install (such as daily compounding) then you will need to make an adjustment: Let: [math]i = (1+\frac{R}{F})^\frac{F}{M}-1[/math] and drop the [math]\times \frac{M}{F}[/math] term in the calculation of X. Note: I made an error in my previous post which I just corrected.

Ok, I will assume that when the bank does its compounding, it will use the largest $ value that was in debt during that period for its interest calculation, that is how most banks work. Given your parameters, P = Principal R = Annual interest rate (eg. 10% = 0.1) F = Compounding periods per year Y = Years until debt is cleared M = M payments per year Find the effective interest per compounding period: [math]i = \frac{R}{F}[/math] Then your regular installment will be: [math]X = \frac{P.i}{1-(1+i)^{-Y.F}} \times \frac{M}{F}[/math] This can easily be rearranged to make the Principal be the subject of the equation if you want to work out how much you should borrow given a certain installment. You can easily test the validity of your result with a scientific calculator: 1. Enter the principal and press "=" 2. Enter the following with the variables replaced with your values: "Ans*i - X*(F/M)" 3. Continually press "=" the number of times that you will make installments, i.e. M*Y times 4. Your calculator should now show 0 (might be slightly off due to rounding errors) If the timescale for paying off this debt is very long, such as a decade or more, then you may consider recalcuating your installments to increase each year in line with inflation, this will allow you to make smaller installments for the early years.

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