████████ ███████

████████ ███████ ███ ███ ████████ █████ ██████ ██████ (█████ ██████ ██████████) ██ ████████. ███ █████ ███, █████████ ████████ █████ ███████ ██ ██████ (██ ██████ ████) █████ ██████ ██ ██████████ █████████ ███ ████████ ██ ███████ ████████ (██████████). ███ ██████ ███-█████ ██ ████████ ███████ ██ ██████ ██████ ██ ███████ ████████████ (██████ ████████ ██████). █████████ ███████ ████ ██████ ██████ ███████ ███ ███ ██████ ███████ ██████ █████ ██ █████ ████████ ███ █████ █████ █████. █████ ██ █████ █████ █████████ ███████ ████. ██████ ███████ ████████ █████████ ███████ ██ ██████ ████████ (█████████ █████████) ███████ ████, █████ (███████).

█████████ ███████ ██████, ██████████ ████████ ███████ ██ ██████ ████████ ██ ████ ██ █████████. ██████, ██████ ███-█████ ██████ ████████ ████-████ ${\displaystyle {\mathbb{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ █████ ██████ █████ ███████ ${\displaystyle (\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})\in {\mathbb{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ ████████: ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}+{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}+{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$. █████ █████ ███ █████ ████████ ███████ ██ ███ ██████████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ █-${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}+{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}+{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$. █████ ██ ███ ████ ███████ ██████ ${\displaystyle \{(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})\in {\mathbb{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}:\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}+{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\}}$.

███ █████ – █████ ██████

████ ██ █ ███ ███. █████████ ███████ ██████ █████ ██ ████ ███ ${\displaystyle \mathbb{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ – ███ ███████ ████████, ██ ███ ███████ ██████ ██████ ██ ██ █ ███ ███ ████ ███████ █████.

████ █${\displaystyle {\mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})}$ (██ ██████ ${\displaystyle {\mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ ██ ████ ████ █) ██ ██████ ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$, █████ ██ █████ ██████ █-█ ████ ███ █. █████ ██ ██████ █"██████ ████████" ████ ███ ██████ ██ ██████ █-${\displaystyle {\mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ ███ ███ ████ ████ ██████, █████ "██████" ██████ ██ ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ █████ ██████. ███████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}:{\mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\to {\mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ █████ ███████ ██ ███ █████ ██████ ████ ███████. █████, ██ ████ ███████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\in \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}[{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}},\dots ,{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}]}$ ██ ████ █████ ${\displaystyle ({\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}},\dots ,{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}})\in {\mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ ██████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}({\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}},\dots ,{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}})=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}({\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}},\dots ,{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}})}$. ████████ ████████ ██ █████ ██████ █-█ ████ ██, ██ ██, █████ █████████ █-█ ██████ ███ █. ██ ████ █████████ █████████ ██ ${\displaystyle {\mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ ████ █-${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}[{\mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}]}$.

████ ██ █ ███ █████ ██ █████████ █-${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}[{\mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}]}$. █████ ████████ ██ █, ███████ █-(█(█ (████ █████ ███ ████ ██ ██████ (█(█), ██████ █████ ████ ██ ███████ █████ ██████ ████ ██ ██████████ █-█ ███████. ██████ █████,

${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})=\{({\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}},\dots ,{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}})\in {\mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}:\mathrm{\forall }\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\in \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}({\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}},\dots ,{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}})=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\}}$.

██ █████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\subseteq {\mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ █████ █████ ███████ ██ █████ █████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\subseteq \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}[{\mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}]}$ ██ █-${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})}$.

████ █████ █████ ████ ██ ███ █████ ████: ██████ ██-█████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\subseteq {\mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$, ███ ████ █████ ██ █████ ██████████ ████████ ██ █? ██ █ ███ ██-█████ █████ ██ ${\displaystyle {\mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$, █████ ██ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})}$ █████ ████ ██ █████████ █████████ ████████ ██ ██ █. ██████ █████, ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})=\{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\in \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}[{\mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}]:\mathrm{\forall }({\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}},\dots ,{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}})\in \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}({\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}},\dots ,{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}})=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\}}$. ████ ██ ██ ██ █ █-█ ███████ ███ █████ █-█ ██ ██ ██ █+█, ███ ██ █ ██████ ███ █████ █-█ ███ █ ███ ███████ ███████ █████, ██ ██ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\cdot \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ ██████ ███ █████ █-█. █████, ███ ██-█████ █ ██ ${\displaystyle {\mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$, ██████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})}$ ███ ██████ ████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}[{\mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}]}$. ███ █████ ███ █████ ██████:

• ██████ ██-█████ █ ██ ${\displaystyle {\mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$, ███ ██████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}))}$?
• ██████ █████ █████████ █, ███ ██████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}))}$?

██ ███ █████ ██ █████ ███████ ███████ ██ █████████ ██████ (██ ██ █████ ██████). ████ █████████ ██ ${\displaystyle {\mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ ██████ ██████ ██ █████ ███████ ██ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}[{\mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}]}$. ██████ ██ █████████ ██████ ███ ███-█████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\subseteq {\mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ ███ █████ █████ ██ ███ ██ █ ███ █████ ███████. ████ ██████ █-${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}))}$ ██ ██ ██ █ ███ █████ ██████████ ██████. ██████ █████ ██████ █████ ██ ███ ████ ██████ ██ ██████. ███ ██████ ████ ██ ████ ██████ ███ █${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}))}$ ████ ██████ ███████ █████ ██ ███ █. ██████ ██ ██████ █ (█████ █-${\displaystyle \sqrt{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$) █████ █████ ████ ██ ███████ █████ █████ ████ █████ █-█, █████ ${\displaystyle \sqrt{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}=\{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\in \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}[{\mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}]:\mathrm{\exists }\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\in \mathbb{<span\; word-length="1"\; class="word\; redacted">█</span>},{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\in \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\}}$. ███████████ ██████ ██████ ██ ███████ ███ ███ █████ ██ ███████ ███████ ██ ██████ ████████ ███████ ██ █, ██ ██ ███████ █████ █████ █████ ██ █████ ██ █████ ██ ██ ████████ ████ █████ ██ ████ ██████. ██████ ███ ████ █████ ██ ███ ██████ ██ ███████ █████ ██ █, ███ ██ ████ █████ ██ ██████ ██ ██████ █${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}[{\mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}]}$ ███ ████ █████.

█████ █████ █████ ████████ █████ ██ █████ ██ ██ ████ ██████ ██████ ██ ███ ███ ██████ ██████ ███████ ██ ███. █████ ███████ ██ █████ █████ █████ ███████. ████ ██████ ██████ ███████ ███ █████ ███████ ██ ███ ██ █████ ██████████ ███████ ████ ███ ██████ ██████.