# Fourier's Theorem/Lemma 1/Mistake 2

## Mistake

... If $M$ is the greatest of the finite numbers $1 M_0 1, 1 M_1 1, \ldots, 1 M_{m - 1} 1$ we have
$\ds 1 \int_a^b \map \psi u \sin N u \rd u 1 < \dfrac {M m} N$

This appears to be an error of transcription from the manuscript to the typeset copy, where absolute value indicators have been interpreted as instances of the number $1$.

... If $M$ is the greatest of the finite numbers $\size {M_0}, \size {M_1}, \ldots, \size {M_{m - 1} }$ we have
$\ds \size {\int_a^b \map \psi u \sin N u \rd u} < \dfrac {M m} N$