NationStates Jolt Archive

How do I make an equation that will reverse the number value that I start with? For example, if I start with 15, I want to end with 1. And if I start with 1, I want to end with 15. Does anyone know anything even close that will help?

Um... the fundamental question is, start what?

uhhhh....

15 - 14 = 1?
1 + 14 = 15?

Inverse operations...

If the initial operation is to add, then the second operation is to subtract the same...

'' multiply '' divide

'' take root to the nth power '' raise to the nth power

etc.

I'm not sure I understand exactly what you're trying to do... using the reciprocal function will get you from 15 to 1, and using the reciprocal of THAT gets you back to 15 again, but I don't really understand what you're trying to do. Why is it 15 that you need to get back to? What's the problem for?

x * 1/x = 1
1 * 1/(1/x) = 1 * x = x

So if you substitute 15 for x then each operation works out via the reciprocal function. I'm still questioning whether I understand the problem accurately, though.

uhhhh....

15 - 14 = 1?
1 + 14 = 15?

Beat me.

How do I make an equation that will reverse the number value that I start with? For example, if I start with 15, I want to end with 1. And if I start with 1, I want to end with 15. Does anyone know anything even close that will help?
You mean- 15 to 51, 51 to 15


Let the tens digit be x, let the ones digit by y.

f(xy)=yx.


Done. :D

Beat me.
I don't do that to other guys.

;)
How about you generate about a billion values with the properties you want, and then run a linear regression on them?
That'll keep you occupied for a few hours.

Obviously I did not make myself clear enough!
I wanted one single equation that will reverse itself.
So if you start with a low number, (it does not have to be 1, I just used that number) your answer will be a high number.
If you start with a high number, (again it does not have to be 15, I just used that number) your answer will be a low number.
But you’re using the same equation each time!
I actually figured it out as I went to bed…
With x being the variable, 16-x. This way if you start with 1 you get 15, and if you start with 15 you get 1. I was tired and can’t believe I didn’t think of this. If you have a better one, good for larger, more complicated equations, I would love to see it!

I don't do that to other guys.

Ahh... but you still do it. Who, or what do you like to beat, may I ask? ;)

How do I make an equation that will reverse the number value that I start with? For example, if I start with 15, I want to end with 1. And if I start with 1, I want to end with 15. Does anyone know anything even close that will help?

I don't really understand what you are asking. What are you trying to do? More examples.

Obviously I did not make myself clear enough!
I wanted one single equation that will reverse itself.
So if you start with a low number, (it does not have to be 1, I just used that number) your answer will be a high number.
If you start with a high number, (again it does not have to be 15, I just used that number) your answer will be a low number.
But you’re using the same equation each time!
I actually figured it out as I went to bed…
With x being the variable, 16-x. This way if you start with 1 you get 15, and if you start with 15 you get 1. I was tired and can’t believe I didn’t think of this. If you have a better one, good for larger, more complicated equations, I would love to see it!

why, exactly, do you need this equation? are you just figuring it out for the hell of it?
what you have there is f(x)=16-x. This is a one-to-one function, because for every x, you have only one f(x), or y, and vice versa...(7,9 9,7 16,0 0,16). basically, anytime you need an equation that reverses the input, a one-to-one function will suffice. this may be wrong, i'm tired too.
but for your equation, if 15 and 1 aren't specified, you can use any constant, not just 16... so it's k-x.
but anyway. i know that was kind of a useless post.

If you have a better one, good for larger, more complicated equations, I would love to see it!
I know one cool equation. I don't know if it would be useful for you but here it goes:

It is called the "Logistic Equation", and it is able to generate CHAOS. Very simple yet very impressive.

f(x) = rx (1 - x)

...where "r" is a constant that you choose before using the equation.
x is the current value and f(x) is the next value (that you can re-inject in the equation at the next iteration).

When r > 3.5699457... (this limit is a transcendental number), and r < 4, you get a chaotic behavior. At each iteration, this function swings around and gives unpredictable results.

This equation was first used to describe the evolution of animal populations, where "r" was the "death versus fertiliy" ratio. It's a good estimate for many animal cycles, especially in situations where food is in limited stocks, the animal has no major predator, and its fertility level is high.

Note: Some values between 3.56... and 4 are periodic, but most of them aren't. What's sad is that you lose precision at each iteration and might get results that aren't totally accurate... unless you used some very-high precision package (such as the one in Java).

Example of use:
r=3.8
x initial = 0.5
f(0.95) = 0.1805
f(0.1805) = 0.562...

http://en.wikipedia.org/wiki/Logistic_map

why, exactly, do you need this equation? are you just figuring it out for the hell of it?


Basically, I am creating a large Microsoft Excel worksheet to figure up multiple equations simultaneously from multiple angles and with multiple alterable values. To explain the whole project would not only take a while, but it would ruin it because I plan on presenting the worksheet to NS eventually. And I’ll just have to re-explain it than.
I thank everyone for their input!

Is this for high school or university (which department)?

Is this for high school or university (which department)?

No, it's for NS. Nation States.