Let \{p_n\} be a sequence of polynomial with finite degree on [0, 1]. If $\forall \epsilon > 0$, $\exists N \in \mathbb{N}$ \newline such that $\forall n, m > N$, $\int_0^1 |p_n - p_m| dx < \epsilon$, then $\exists p$ such that $p_n \to p$ uniformly.
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We are given a sequence of polynomials {pn} with finite degree on the interval [0,1]. This means that each polynomial pn(x) can be written as pn(x) = anxn + an-1xn-1 + ... + a1x + a0, where an, an-1, ..., a1, a0 are constants and n is the degree of the polynomial. Show more…
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