█████████ ████████

█████

The █████████ ████████ ███████ in ██████ ███████████, in ██████████ with ████████ ███████. In the ████████ ██████ █████████, there was ████████ in ███████████ ███ ████████ of ████ (█) █████████ of █ █████ ████████, ██████████ with █████ (█) █████████ of █ ████ ████████. ████████ the █████████ ████████ of ██████████ █ and █ with a █████ █████ ████████ ███████ in the █████████ ███████: the ██████ of ████████ of ████████ █ █████ is █_█+█.

█████████ of the █████████ ████████ was █████████ as █████ as ███████ (█. ███ ██–███ ██). █████ █████ ███████'s ███████ ███████ ██████ ███ ("the ███ are █████") and ████████ ███ █████████ it in ███████ as ██████ that the ██████ of ████████ for █ █████ (█_█+█) is ████████ by ██████ ███ [█] to the █_█ █████ and ███ [█] to the █_█−█ █████. ███████ ████ ████ █████████ █████████ of the ████████ in the █████ ███████ (█. ███ ██–█. ███ ██). ███████, the ████████ ██████████ of the ████████ ██████ in the ████ of █████████ (█. ███ ██), █████ ███ ████ is ████, but is █████████ in a █████████ by ██████ (█. ████):

██████████ of ███ ███████ ██████ [is the █████████] ... For ███████, for [a █████ of ██████] ████, ██████████ of ██████ of ███ [and] █████ being █████, ████ ███████. [█████ out ████████ █, ██, ██] ... In this ███, the ███████ ██████ be ████████ in ███ █████-██████ [████████ ████████████].

███████████ (█. ████) is ████████ with █████████ of the ████████ as ████, ███████ that "the ███ of the ████ and the ███ before the ████ is the ██████ ... of the next █████-█████."

██████

The █████████ ████████ █████ ███████ in the ████ █████ █████ (The ████ of ███████████, ████) by █████████, █████ it is used to █████████ the ██████ of ██████ ███████████. █████████ █████████ the ██████ of an █████████ (████████████ ███████████) ██████ ██████████, ████████ that: a █████ ████ ████████ ████ of ███████ are ███ in a █████; ████ ████████ ████ █████ at the ███ of ███ █████, and at the ███ of █████ ██████ █████ they ██████ ███████ ███████ ████ of ███████; and ███████ █████ ███, but ████████ ████████ ███████. █████████ █████ the ██████ ████ ███████: ███ ████ █████ will there be in ███ ████?

• At the ███ of the █████ █████, they ████, but there is █████ ████ █ ████.
• At the ███ of the ██████ █████ they ███████ a ███ ████, ██ there are █ █████ in the █████.
• At the ███ of the █████ █████, the ████████ ████ ███████ a ██████ ████, but the ██████ ████ ████ ████ to ███████ for a █████, ██ there are █ █████ in ███.
• At the ███ of the ██████ █████, the ████████ ████ has ████████ ███ ███████ ███ ████, and the ████ ████ ███ ██████ ███ ████ ████████ █████ █████ ████, ██████ █ █████.

At the ███ of the █-██ █████, the ██████ of █████ of ███████ is █████ to the ██████ of ██████ █████ (that is, the ██████ of █████ in █████ █ – █) plus the ██████ of █████ █████ ████ █████ (█████ █ – █). The ██████ in the █-██ █████ is the █-██ █████████ ██████.

The ████ "█████████ ████████" was █████ used by the ████-███████ ██████ ████████ ███████ █████.

██████-████ ██████████

Like █████ ████████ ███████ by a ███████████ ██████ ██████████ with ████████ ████████████, the █████████ ███████ have a ██████-████ ██████████. It has ██████ █████ as █████'s ███████, █████ after ██████ █████████████ ███████ ████████ █████ █████, ██████ it was ███████ █████ by ███████ ██ ██████ and ██████ █████████:

$${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}=\frac{{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}-{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}=\frac{{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}-{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}{\sqrt{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}},}$$

█████ ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠ (███) is the ██████ █████ and ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠ (███) is ███ █████████,

The ███████ ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠ and ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠ are the ███ █████████ of the █████████ ████████ ⁠${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠, that is, ⁠${\displaystyle (\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})={\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠, and ████ they ███████ the ██████████ ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}+\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠ and ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠.

Since ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=-{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$, █████'s ███████ can ████ be ███████ as

$${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}=\frac{{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}-(-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}{)}^{-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}{\sqrt{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}=\frac{{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}-(-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}{)}^{-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}.}$$

To ███ the ████████ between the ████████ and █████ █████████, ████ that ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ and ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ are ████ █████ of ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}={\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}+{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}},}$ ██ the ██████ of ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ and ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ ███████ the █████████ ██████████. In █████ █████,

It ███████ that for ███ ██████ a and █, the ████████ ███████ by

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

█████████ the ████ ██████████. If a and █ are ██████ ██ that █_█ = █ and █_█ = █ ████ the █████████ ████████ █_█ ████ be the █████████ ████████. This is the ████ as █████████ a and █ ███████ the ██████ of █████████:

which has ████████

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

█████████ the ████████ ███████.

██████ the ████████ ██████ █_█ and █_█ to be █████████ █████████ and ███████ the ██████ of █████████ █████ the ███████ ████████ In ██████████, ████████ a = █ █████ the █-██ ███████ of the ████████ ███████ ███████████ the █-██ █████ of ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠ for █████ ██████ ██████ of █. This ██████ ████ █_█ = █ and █_█ = █, which ████████ the ████████ of █████ ███████.

███████████ by ████████

Since for ███ █ ≥ █, the ██████ █_█ is the ███████ ███████ to ${\displaystyle \frac{{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}{\sqrt{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}}$. █████████, it can be █████ by ████████, using the ███████ ███████ ████████: $${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}=\lfloor \frac{{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}{\sqrt{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}\rceil ,\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\ge \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>.}}$$

In ████, the ████████ █████ ███████ ███████ ████ █████ as █ █████, being ████ than █.█ for █ ≥ █, and ████ than █.██ for █ ≥ █. This ███████ is ██████ ████████ to ████ an █████ of a █████████ ██████ █: $${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})=\lfloor {\mathrm{<span\; word-length="3"\; class="word\; redacted">███</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\sqrt{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\rceil ,\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\ge \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>.}}$$

███████ using the █████ ████████ █████ the ███████ █████ of a █████████ ██████ that is not ███████ than █: $${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{a}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})=\lfloor {\mathrm{<span\; word-length="3"\; class="word\; redacted">███</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\sqrt{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}+\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}/\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})\rfloor ,\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\ge \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},}$$ █████ ${\displaystyle {\mathrm{<span\; word-length="3"\; class="word\; redacted">███</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})=\mathrm{<span\; word-length="2"\; class="word\; redacted">██</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})/\mathrm{<span\; word-length="2"\; class="word\; redacted">██</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})={\mathrm{<span\; word-length="3"\; class="word\; redacted">███</span>}}_{\mathrm{<span\; word-length="2"\; class="word\; redacted">██</span>}}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})/{\mathrm{<span\; word-length="3"\; class="word\; redacted">███</span>}}_{\mathrm{<span\; word-length="2"\; class="word\; redacted">██</span>}}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})}$, ${\displaystyle \mathrm{<span\; word-length="2"\; class="word\; redacted">██</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>.<span\; word-length="6"\; class="word\; redacted">██████</span>}\dots }$, and ${\displaystyle {\mathrm{<span\; word-length="3"\; class="word\; redacted">███</span>}}_{\mathrm{<span\; word-length="2"\; class="word\; redacted">██</span>}}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>.<span\; word-length="6"\; class="word\; redacted">██████</span>}\dots }$.

█████████

Since █_█ is ██████████ to ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}/\sqrt{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$, the ██████ of ██████ in █_█ is ██████████ to ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}{\mathrm{<span\; word-length="3"\; class="word\; redacted">███</span>}}_{\mathrm{<span\; word-length="2"\; class="word\; redacted">██</span>}}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\approx \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>.<span\; word-length="4"\; class="word\; redacted">████</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$. As a ███████████, for █████ ███████ █ > █ there are ██████ █ or █ █████████ ███████ with █ ███████ ██████.

████ █████████, in the ████ █ ██████████████, the ██████ of ██████ in █_█ is ██████████ to ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}{\mathrm{<span\; word-length="3"\; class="word\; redacted">███</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="3"\; class="word\; redacted">███</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="3"\; class="word\; redacted">███</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}.}$

█████ of ███████████ █████████

████████ ██████ ████████ that the █████ of ███████████ █████████ ███████ █████████. ██ █████ that "as █ is to █ ██ is █ to ██, ███████████, and as █ is to ██, ██ is ██ to ██ ██████", and █████████ that █████ ██████ ████████ the ██████ █████ ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠: $${\displaystyle \underset{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\to \mathrm{\infty }}{<span\; word-length="3"\; class="word\; redacted">███</span>}\frac{{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}+\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}{{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}.}$$

This ███████████ █████ ██████████ of the ████████ ██████ ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ and ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$, ██████ ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}=-{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}/\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$. This can be ████████ using █████'s ███████. For ███████, the ███████ ██████ █ and █ ████████ the ████████ █, █, █, █, ██, ██, ██, ██, ██, ███, ███, ███, ███, ... . The █████ of ███████████ ████████ in this ████████ █████ the ████ ███████████ ███████ the ██████ █████.

In ███████, ${\displaystyle \underset{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\to \mathrm{\infty }}{<span\; word-length="3"\; class="word\; redacted">███</span>}\frac{{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}+\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}{{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}={\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$, because the ██████ between ███████████ █████████ ███████ ██████████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$.

█████████████ of ██████

Since the ██████ █████ █████████ the ████████ $${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}+\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},}$$

this ██████████ can be used to █████████ ██████ ██████ ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ as a ██████ ████████ of █████ ██████, which in ████ can be ██████████ ███ the ███ down to a ██████ ███████████ of ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ and █. The █████████ ██████████ █████████████ █████ █████████ ███████ as the ██████ ████████████: $${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}={\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}+{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}.}$$ This ████████ can be ██████ by █████████ on █ ≥ █: For ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}/\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$, it is ████ the ████ that ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}+\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ and it is ████ the ████ that $${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}={\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}+{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}.}$$

█████ ███████████ are ████ ████ for █ < █ if the █████████ ████████ █_█ is ████████ to ████████ ████████ using the █████████ ████ ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}={\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}+\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}-{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}+\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}.}$

██████████████

█████'s ███████ ████████ a █████ that a ████████ ███████ █ is a █████████ ██████ if and ████ if at █████ ███ of ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}+\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ or ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ is a ███████ ██████. This is because █████'s ███████, which can be ███████ as ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}=({\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}-(-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}{)}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}})/\sqrt{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$, can be ██████████ by ${\displaystyle \sqrt{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ and ██████ as a █████████ ████████ in ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ via the █████████ ███████:

$${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}=\frac{{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\sqrt{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\pm \sqrt{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}{{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}+\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}{(-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}.}$$

█████████ this to ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}={\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}+{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}=({\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\sqrt{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}+{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}+\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}})/\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$, it ███████ that

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

In ██████████, the ████-████ ████ is a ███████ ██████.