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**dimischka****Guest**

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.

**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

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..."

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**dimischka****Guest**

Thank you.

How about convergence to a solution, is that provable?

**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

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..."

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**dimischka****Guest**

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.

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