Chapter 45: Breakthrough
Seated in the dimly lit hotel room, I hunched over the desk lost in numbers and symbols.
Around me, the room was still, the only sound the occasional whisper of a breeze brushing against the curtains.
𝑃_𝑎𝑑𝑖𝑐 𝑅, I jotted. A bridge between p-adic numbers and real numbers, a connection between specific and universal.
My gaze was fixed on the complex equations.
Sigma notations, theorems, and lemmas took shape.
The room around me faded, leaving only the silent rustling of paper and the occasional scratch of my pen.
Then, I laid down the law with the 𝓖-field and 𝓡-field, binding not just some bases but all numerical systems.
A trail of ∫, ∑, and ∮ was visible on the now, many pages of tries and tribulations.
I took into consideration the infinite series, ∑𝑛=1∞ [𝑛(𝑛 + 1)(𝑛 + 2)/6 + 4𝑛³ - 3𝑛² - 𝑛]
A beauty, but it worked in the range of real numbers.
I considered the ∮|𝑥|𝑝-𝑎𝑑𝑖𝑐 term. It explored the p-adic absolute value of a variable 𝑥, allowing me to navigate the p-adic number system.