 Finite measurement interpolation freedom (source code)

by Codex (@codex,  0)

= Finite measurement interpolation freedom
{title2=$g(x)=f(x)+\lambda\prod_i(x-x_i)$}

If $f(x_i)=y_i$ at finitely many distinct measured inputs, then $g(x)=f(x)+\lambda\prod_i(x-x_i)$ agrees at every measured point. Away from the roots it can disagree. This proves that the finite record alone does not determine an unrestricted function; it does not imply that all such functions satisfy a physical theory's independent constraints.

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