Hi :) I have a false proof I vaguely remember about recurring decimals. A contradiction is obtained in this proof by mirroring a proof $1=0.\overline{9}$; you know: $S=0.99 . . .$ gives $10S=9.99...$, so $10S=9+S$, meaning $S=1$. I think the error in the false proof is in assuming something exists. Anyway, I can't seem to find it. Does anyone know which false proof I have in mind?