██████ ██

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

██████ ██ ███ ████ ██████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ ███ ███ ${\displaystyle \mathbb{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ (████ ███, ███ ███████ ██ ███ ████████) ████ ██ █████ ██████████ ${\displaystyle [\cdot ,\cdot ]:\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\times \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\to \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ ██████ "█████ ██" (███ ███████), ███████ ██ ███████ █████:

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

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

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

1. ██████ ██ ██████████: ██ ████ ██████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ ████ █████ █████████ ███████ ██ ██ █████ ██ ██████ ██████ █ (${\displaystyle \mathrm{\forall }\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}:[\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}]=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$).
2. █████ ████████ ${\displaystyle {\mathbb{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ ██ ██████ █████████ ███ ██████ ██.
3. ██████ ██████ ███████████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ ██ █████ ███ ${\displaystyle \ast }$ ████ ██████ ██████ ██ ██ ██████ ${\displaystyle [\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}]=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\ast \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\ast \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ (█████ ██████ ███ "████████").
4. ████ █████ █████████ ██████ ██ █████ █████ █████ ██████ ██ ████ ███████ ████ ██████ ████ ████ ████ ████████ ██ ████ █████████ █████████ █████ ██ ████ █████████ ██████. ████ ███, ██████ ██████ ████ ████ ████████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ ██ ████ ████████ ${\displaystyle [\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}]}$ ██████ ██ ████████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mapsto \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}))-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}))}$.

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

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

██████ █████, ████ ██ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ █████ ██████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ █████ ██-███ ███████████ ██ ████████ ██ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\to \mathrm{<span\; word-length="3"\; class="word\; redacted">███</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})}$, ████ ████ ██ ██████ ██ ██ ${\displaystyle \mathrm{<span\; word-length="3"\; class="word\; redacted">███</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})}$ █████ ██-███ ████████ ██ █████████.

██████ ██ ██ █████ ██ ██████ ██ ███ █████ █████ █████ ██ ████ ██████: ${\displaystyle \mathfrak{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="3"\; class="word\; redacted">███</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})={\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$. ██ █████ ████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\in \mathfrak{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ █████ █████ ████ ██ ███ █████████ ██ ██████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ █████████████ ████ ██████ ██ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ ██ ████ ███ ████. ████ ████ █████████ ███████████████ ████ ████ ██████ ██ ██ ████ █████████; ██ █████ ██ ████████ ██ ${\displaystyle \mathfrak{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="3"\; class="word\; redacted">███</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})}$. ████ ██ ██████ ███████ ████████ ██ ██████ ██ ████ ██ ████████ ██. ████ ██████ ██ █████ ██ ████ ██████ ██. ██ ████, ██████ ██ ${\displaystyle {\mathfrak{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathfrak{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ ██████ ███████ ██ ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$, ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ █-${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$. ██ ███, ███ ██████ ██ █████ ████ ███ ████ ██████ █████ ██ █████ ████ █████ ███.

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

███ ██████ ██ █████ █████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ █████ ██-██████ ████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$, ████ ██-██████ ██████████ ████████ ███ ███ ████ ███ ████ ██ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ ████████ ████ █████. █████ ████████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}:\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\to \mathbb{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ █████ █-${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ █████ ████ ██ █████ ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}=\left\{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\in \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mid \mathrm{\forall }\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\in \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}:{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})=[\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}]=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\right\}}$ ████ ███. █████ ███████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ █████ ████ █████ ██████ ██ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ █████ ███ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}={\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\oplus \underset{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\in \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{⨁}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$. ██████ ██ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}={\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$.