When we were shown that Taylor’s series had the best match, I remained silent because I trusted the band.
When on the theory of the rows we were proved that the Fourier rows had the best convergence, I remained silent, because I found no error in the proof.
When the same poker facet showed us that Chebyshev's polynoms had the best match, I remained silent, because it was too late to argue.

[Later it turned out that all three statements are true, only the criterion by which the "best convergence" is determined changes.]