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polynomials are continuous

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Statetement

Given a polynomial P[X]P \in \mathbb{R}[X] over the real numbers, we may regard it as a function P:P \colon \mathbb{R} \longrightarrow \mathbb{R}. If here \mathbb{R} is regarded as a Euclidean space (equipped with its metric topology), then this is a continuous function.

References

The proof using epsilontic analysis is spelled out for instance in

  • Kyle Miller, Polynomials are continuous functions, 2014 (pdf)

Last revised on May 7, 2017 at 10:18:42. See the history of this page for a list of all contributions to it.