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## #1 2006-01-27 03:07:43

dimischka
Guest

### Solving a system on nonlinear equations

Can we prove the existence of a unique solution of a square system of nonlinear equations? Where the number of equations equal the number of constraints and all equations are indepedent.

## #2 2006-01-27 05:02:10

Ricky
Moderator

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### Re: Solving a system on nonlinear equations

Consider the square, nonlinear, independant equations:

x² + y² = 0
x² + y² = 1

In short, the answer is no.

"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

## #3 2006-01-27 05:29:25

dimischka
Guest

### Re: Solving a system on nonlinear equations

Thank you.

How about convergence to a solution, is that provable?

## #4 2006-01-27 05:35:15

Ricky
Moderator

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### Re: Solving a system on nonlinear equations

Convergence of a solution?  Convergence is normally described for a function, not an equation.  I'm not sure what you mean by convergence in this context.

"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

## #5 2006-01-27 05:41:16

dimischka
Guest

### Re: Solving a system on nonlinear equations

Sorry I'm not articulate enough.

What I meant is if I have a set of nolinear equations, how can I prove that there is indeed a solution to that system?

Thanks.