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I have a basic question about convergence.

I have two sequences, x_{1}, x_{2}, ... and y_{1}, y_{2}, ..., where y_{n}= f(x_{n}) for some function f : ℝ^{N}→ ℝ.

I have shown that the sequence, y_{1}, y_{2}, .... converges. What conditions do I need on the function, f, to ensure that the sequence x_{1}, x_{2}, ... also converges?

Thanks in advance

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# A Simple Convergence Question

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