The following inequality is transformed by someone as follows:

$$
\begin{aligned}
& \frac{1}{4}>\frac{1}{8} ; \quad\left(\frac{1}{2}\right)^{2}>\left(\frac{1}{2}\right)^{3} \\
& 2 \lg \frac{1}{2}>3 \lg \frac{1}{2}, \quad \text { therefore } \quad 2>3
\end{aligned}
$$

Where is the mistake?
The error is in the last step. Indeed, $\lg \frac{1}{2}<0$, and thus dividing both sides by it reverses the inequality: $2<3$.

Kesselyák Mihály (Szeged, Radnóti g. I. o. t.)