Multime finita de numere complexe de forma |a^n-b^n|
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Multime finita de numere complexe de forma |a^n-b^n|
Se considera numerele complexe \( a\neq b \) si multimea \( A=\{ |a^n-b^n|, n\in\mathbb{N}^{*} \} \). Sa se demonstreze ca daca \( A \) este finita, atunci \( |a|=|b|=1 \) si \( 0\in A \).
An infinite number of mathematicians walk into a bar. The first one orders a beer. The second orders half a beer. The third, a quarter of a beer. The bartender says “You’re all idiots”, and pours two beers.