# Expressing loops etc. in math.

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• 07-17-2002
sean
Expressing loops etc. in math.
Well I'm still working on that universal equation thing. I have a series of equations, all related - like a series of steps to take - one follows the other. I calculate the value of a variable, r, based on x. If r is equal to 1, then I finish up the calculation because I know everything is set up right. If not, then I want to increase d by 1, and then repeat the calculation. Is there a standard mathematical way of expressing this?

And one more question: In multivariable-differential calculus, if your calculating dy/dx as x->0, couldn't you just add one to the exponent of each x in the equation of change in y/change in x? It seems to work and is a lot simpler than waht my book says.
• 07-17-2002
MethodMan
Re: Expressing loops etc. in math.
Quote:

Originally posted by Sean
Well I'm still working on that universal equation thing. I have a series of equations, all related - like a series of steps to take - one follows the other. I calculate the value of a variable, r, based on x. If r is equal to 1, then I finish up the calculation because I know everything is set up right. If not, then I want to increase d by 1, and then repeat the calculation. Is there a standard mathematical way of expressing this?

And one more question: In multivariable-differential calculus, if your calculating dy/dx as x->0, couldn't you just add one to the exponent of each x in the equation of change in y/change in x? It seems to work and is a lot simpler than waht my book says.

I dont know the answer to the first question, but the second one sounds familiar, what section is it under, so I can take a look, I may be able to help out a little more.
• 07-17-2002
toaster
express loops mathematically?

remember the "E" thingy as in:
Code:

``` n<stuff E( stuff ) n=0```
as to make a mathematical formula out of your problem, I'm unable to do right now since I'm currently brain dead. I'll try to respond again when my headache is over.
• 07-17-2002
Xterria
WHAT DOES THAT E(greek sigama) ACTUALLY DO IN MATH?!?!?! I'VE LOOKED EVERYWHERE AND THEY GIVE ME GARBAGE ANSWERS?!!!!!!!!!!!!!!

boo hooo
• 07-17-2002
MethodMan
Quote:

Originally posted by Xterria
WHAT DOES THAT E(greek sigama) ACTUALLY DO IN MATH?!?!?! I'VE LOOKED EVERYWHERE AND THEY GIVE ME GARBAGE ANSWERS?!!!!!!!!!!!!!!

boo hooo

It symbolizes sum.
So
n = 0
E (n = n+1)
n = 10

so a sum from 0 to 10, substituting n into the equation in ()
• 07-17-2002
Xterria
wtf? 0+1 is not 10!
help?
• 07-17-2002
MethodMan
Quote:

Originally posted by Xterria
wtf? 0+1 is not 10!
help?

You start with n = 0, and you go up to n = 10

so the equation is n = n+1, or u can say k = n +1
so k = 1 (n=0), 2 (n = 1), 3 (n = 2)
• 07-17-2002
toaster
Re: Expressing loops etc. in math.
Quote:

Originally posted by Sean
Well I'm still working on that universal equation thing. I have a series of equations, all related - like a series of steps to take - one follows the other. I calculate the value of a variable, r, based on x. If r is equal to 1, then I finish up the calculation because I know everything is set up right. If not, then I want to increase d by 1, and then repeat the calculation. Is there a standard mathematical way of expressing this?

And one more question: In multivariable-differential calculus, if your calculating dy/dx as x->0, couldn't you just add one to the exponent of each x in the equation of change in y/change in x? It seems to work and is a lot simpler than waht my book says.

that's a hectic thing to follow. I should take back my words I said when I was in pain. first I do believe anything, but limited, expressed in programming can be translated into mathematical terms. however, making formulas can be quite fustrating at times. since I do not exactly know how the calculations are, I can try with the series and a function and play around with it and add other terms if necessary. maybe I can start by making the function control how the series goes (all those complex algorithms). I might as well not continue with the stuff I do not understand that I am saying.

anyway, with the limts that u were talking about, the values get closer and closer to a value (for when very precise values are needed). I forget but Dalton might be one of the first to start the idea with limits or something. the book is a reference telling you exactly how the thing works. shortcuts? I think there are plenty for this but sometimes they don't work for certain problems.

I think I need to rest before I continue (this is what vacation does to people). :(

reference I suggest:

http://mathworld.wolfram.com/

also, these guys (professionals) might help out at :

http://www.mathforum.org/dr.math/
• 07-18-2002
sean
Exterria - it symbolizes sum, but it's usually only used with differentiation. For example, if you have a series (pretend that any number preceded by a \ is subscript), you can get the sum. Say n is as follows: n \1 = 1, n\2 = 2 n\3 = 4, n\4 = 8 n\5 = 16.
En (with a superscript 1 and a subscript 5 below it) would equal 1 + 2 + 4 + 8 + 16 = 31.

I've considered using that in a variety of ways, but what I need to do is perform all the calulations with d=1, and if r != 1 then I need to increment d and do all the calculations again. It's a series of equations that all follow off from eachother.
• 07-18-2002
Govtcheez
> but it's usually only used with differentiation.

You mean integration? (since, AFAIK, the integral symbol's meant to look like an S, for Sum)
• 07-18-2002
sean
And also, no, 0+1 does not equal 10, but it would if we could get a mathematical loop in there - that's the kind of loop I'm talking about just to repeat I can just put another equation in there easily to increment d. (i.e. d=d+d) ^=delta. So does anyone know of any place they've seen of repeating a calculation? Sigma is close but it's just not quite solving the problem the ways I've tried it. Thanks for the help so far though.
• 07-18-2002
Shiro
You mean such like this?

Code:

```Pre: true Post: {r == 1} d = ? r = ? while (r != 1) do begin     r = f(x)     {(r == 1 || r != 1) <-> true}     if (r == 1)         {r == 1}         break;     else         {r != 1}         d = d + 1 end {r == 1}```
This is not complete, since there is no information available about variable d.

>In multivariable-differential calculus, if your calculating dy/dx as
>x->0, couldn't you just add one to the exponent of each x in the
>equation of change in y/change in x?

?

y = x^n
dy/dx = n x^(n-1)
• 07-18-2002
sean
First answer: I mean pure mathematical - no programming.

Second answer: My fault actually - I meant single-variable. I actually didn't need to post that - I had it right here in my book! Thanks anyway.
• 07-21-2002
sean
One other thing.... well two other things:

1) Are there just 4 degrees of equations, or is their an infinite amount?

2) If it is just four, I could write out the equation for times, and then have some way of testing the value of a variable, like the if statement, but again, it would have to be completely mathematical.

And in response to the original question's answers - I was thinking about the sum thing - if I summed all the possibilties, divided them by four (again - dependant on there only being four degrees), that would just be the average. But if I could get an equation that modified the average dependant on the degree, then it would work. Anyone?
• 07-21-2002
salvelinus
Shiro, I think you're mixing languages. No "begin" or "end" in C++, also need some ;'s at the end of statements.
As far as the math, no idea.
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