Prove that Rademacher system $\{r_n=sign(\sin(2^n\pi t)\}$ is not complete system in $L_2[0,1]$. I have some problems with proving this. I think, I should take a function $f\ne0$ such that $<f,r_n>=0$. I have no idea how to choice such function
2026-04-01 18:34:32.1775068472
A question about Rademacher system
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Here's a hint. Try $f=r_1 r_2$. More generally, try sketching the graphs of as many of the $r_n$ as you can without getting bored, and see if you can spot why this suggested $f$ is orthogonal to all the $r_n$.