Chapter One: A Strange Encounter

The blazing summer sun hung high in the sky, bathing the afternoon in a restless heat that seemed to press against every surface. Even the cicadas had lost the strength to sing. Wu Tong sat at her desk, the air conditioning set to twenty-five degrees, cold air circulating throughout the room, yet she still felt unbearably agitated.

Given the universal set U equals R, set M equals the collection of integers x such that negative one is less than or equal to x minus one is less than or equal to two, and N equals the collection of x such that x equals twice k, where k is an integer, the relationship Venn diagram is as shown. How many elements are there in the shaded region of the diagram?

How many are there?

Wu Tong truly had no idea. At twenty-eight, a working adult who had left the classroom a decade ago, how could she possibly remember high school mathematics problems? Frowning, she rubbed her brow in frustration; who could have anticipated that she would awaken from unconsciousness to find herself back in the summer break of her first year of high school, transformed into a willful, ignorant, and unmotivated academic underachiever?

Her head throbbed painfully, scenes of her father's fatal car accident and her mother hovering between life and death in the emergency room flashed across her mind. Her heart seemed seized by an invisible hand—an agonizing pain that made it difficult to breathe.

Suddenly, the pen in her hand snapped against the desk. Wu Tong looked at the test paper before her.

Everything could still be changed.

It was only 2009; she was sixteen, still before the college entrance exams!

Wu Tong forced herself to concentrate, even entertaining the fanciful notion that if only something existed to help her focus, to clear her mind and let her study undistracted, it would be wonderful!

She was about to mock her own inability to focus, not even asleep and already daydreaming!

Abruptly, a cool, tranquil sensation spread from deep within her mind, enveloping her like biting into a chilled watermelon on the hottest day of summer—refreshing and invigorating.

For a brief moment, the difficult problem that had just troubled her seemed to unravel; from the depths of her limited knowledge, she grasped a few threads of insight—perhaps she should approach it from the intersection of sets M and N.

Was this a windfall from the heavens?

Or merely a hallucination?

If it were an illusion, then the solution emerging in her mind was certainly real—it was knowledge she absolutely could not recall at this time, though the teacher had covered it back then, she’d never paid close attention.

Now, undistracted, the forgotten points were dredged up, connected from dots to lines, forming a coherent train of thought for solving the problem.

In a word, it was the spark of inspiration.

If possible, Wu Tong hoped this was genuine, and not a one-time occurrence.

To test it, she calmed herself and reread the question; the same lucid clarity welled up again, banishing all distracting thoughts and leaving only a single-minded determination to solve the problem. She began to write, following her new line of reasoning.

The shaded region in the diagram represented the intersection of M and N...

Given M is the set of real numbers x such that negative two is less than or equal to x minus one is less than or equal to two, which simplifies to negative one is less than or equal to x is less than or equal to three, and N is the set of x such that x is twice k, with k an integer.

Thus, their intersection is the set containing zero and two.

Therefore, the shaded region contains two elements.

Writing fluently and confidently, the answer emerged beneath her pen. Wu Tong felt the exhilarating satisfaction of solving a problem.

If learning could always be this comfortable, then studying would be a joyful pleasure, not a torment!

The gift of inspired writing—how many people yearn for it!

Such an unexpected fortune filled Wu Tong with delight, but also curiosity and doubt: where had this opportunity come from? Recalling the strange sensation that had originated deep in her mind, she closed her eyes, calmed herself, and focused inward to explore further.

As her heart settled, Wu Tong’s consciousness seemed to arrive in a wondrous place, her thoughts clear, a wave of understanding rising within. It was the deepest part of her mental sea, and within it, a slightly damaged, dark jade stele stood tall. Even with its flaws, the stele shone with a gentle, luminous radiance.

Wu Tong’s consciousness tentatively approached the stele, and was enveloped by its steady, mountain-like aura; a warm current quietly flowed into her heart, and the entire sequence of events unfolded naturally before her.

There exists a mystical object in the world, known as the Enlightenment Stone, naturally formed as a stele, with the remarkable effect of comprehending the ultimate principles of heaven and earth. Yet, as time passed, and the years wore away, the stele’s once-great powers had dwindled to a mere trickle—now all that remained was its ability to calm the mind, concentrate thoughts, and assist in reasoning and error correction, barely clinging to existence.

Today, activated by the crisscrossing energies of time and space, it had unexpectedly enabled its owner, Wu Tong, to awaken memories of her previous life, merging past and future, granting her a glimpse into what was yet to come.

For Wu Tong, even these minor abilities were precious aids; to possess them was her good fortune, and she had no greedy desire to ascend in a single leap, to become immortal or divine.

All tragedy had begun after that summer break, when she deliberately neglected her studies. Now, with the warning of her past life’s memories, and the aid of the Enlightenment Stone, the first step to changing her fate was clear: she must study diligently.

Step by step, she would learn solidly, master more knowledge, become the pride of her parents, become a useful person, able to direct her own life. This was the path her parents most wished for, and it was the best road for her development.

In her previous life, she had been exhausted by repetitive work, never truly understanding the world. She knew future technology would leap forward, but not the principles behind it; she knew that housing prices in major cities would soar, but her family lacked the capital to buy property there.

She knew some people would win the lottery, tens of millions or even billions, but her memory did not include the winning numbers.

Her family was as ordinary as most, living in the small county of Xincheng in Tianzhong City, Central Plains. Her father, Wu Jingzhong, was a civil servant working at the county agricultural bureau; her mother, Jin Yu, was an elementary school teacher, teaching mathematics. The family was not wealthy, but their basic needs were met.

They did not pursue extravagance, nor were they in any major financial difficulty, so she did not need to immediately rush out and earn money.

There is gold in books; studying well is also a way to earn a living.

She had heard, in her previous life, of a mathematician who solved a mathematical conjecture and was rewarded with a million yuan.

She did not know her own limits, but by temperament, she was not skilled at social interaction; work that required research and focus suited her best. Now, with the Enlightenment Stone’s assistance, perhaps she could reach such heights!

Moreover, diligent study and comprehension of knowledge would nourish and restore the Enlightenment Stone, forming a mutually beneficial relationship.

Apart from its origin, the Enlightenment Stone also bestowed upon Wu Tong a method for strengthening her body, which she named the Rising Sun Purple Qi Technique. Using herself as the medium, she would absorb the purple qi of the morning sun each day, paired with special breathing, circulating it through her limbs and bones, nourishing every part of her body. While it did not grant miraculous abilities, it would strengthen her muscles and bones, enhance her constitution, and ward off serious illness.

Regrettably, absorbing the morning purple qi was suitable only for her, as it required resonance between the stele and her own mind. However, she could study and simplify the breathing method, and teach it to her parents, combined with gentle exercise, to strengthen their bodies. With improved health, illness would trouble them less, and at the very least, they could strive to live past a hundred years, passing peacefully and free from disease.