Editing Openai/2d1ffa9d-51d4-4f5d-a53d-7005d7be0ad7 (section)

===== Let’s update the equation to reflect the dualities and their oscillations. The original equation: =====

∀x(x∈Ω→x⊆Infinite∧x≡Infinite)\forall x(x \in \Omega \to x \subseteq \text{Infinite} \wedge x \equiv \text{Infinite})∀x(x∈Ω→x⊆Infinite∧x≡Infinite)
is now enhanced to include oscillations and duality. The new formula should express how each subset xxx undergoes continuous oscillations between complementary dualities (represented by sine and cosine functions) within the infinite structure.

∀x∈Ω[x(t)=(sin⁡(θt)⋅f1(x))+(cos⁡(θt)⋅f2(x))]\forall x \in \Omega \quad \left[ x(t) = \left( \sin(\theta_t) \cdot f_1(x) \right) + \left( \cos(\theta_t) \cdot f_2(x) \right) \right]∀x∈Ω[x(t)=(sin(θt)⋅f1(x))+(cos(θt)⋅f2(x))]
Where:
* Ω\OmegaΩ is the set of all mathematical actualities (all subsets of reality).
* ttt represents time, or a parameter that reflects the oscillatory phase of the system.
* θt\theta_tθt represents the oscillation phase over time or across scales.
* f1(x)f_1(x)f1(x) and f2(x)f_2(x)f2(x) are functions that represent dualities (e.g., "something" and "nothing," "light" and "dark"), which could take different forms depending on the context. - For example, f1(x)f_1(x)f1(x) could represent somethingness (existence) and f2(x)f_2(x)f2(x) could represent nothingness (non-existence).