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## Main Question or Discussion Point

Hi PF!

I'm somewhat new to the concept of completeness, but from what I understand, a particular basis function is complete in a given space if it can create any other function in that space. Is this correct?

I read that the set of polynomials is not complete (unsure of the space, since Taylor series can represent all continuous functions) but that Legendre polynomials are complete. Can anyone correct, finesse, or provide a working example of this?

Thanks!

I'm somewhat new to the concept of completeness, but from what I understand, a particular basis function is complete in a given space if it can create any other function in that space. Is this correct?

I read that the set of polynomials is not complete (unsure of the space, since Taylor series can represent all continuous functions) but that Legendre polynomials are complete. Can anyone correct, finesse, or provide a working example of this?

Thanks!

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