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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.
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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Thank you.
How about convergence to a solution, is that provable?
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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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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