The summer sun blazed down in the sky, and the afternoon air was filled with an unbearable heat, so intense that even the cicadas had lost their energy to chirp. Wu Tong sat at her desk, the air conditioner at 25 degrees Celsius, blasting cool air through the room, yet she still felt unbearably restless.
Given the universal set U=R, the set M={x∈Z|-1≤X-1≤2}, and the relationship between N={x|x=2k, k∈Z}, the Venn diagram is shown in the figure. How many elements are there in the set indicated by the shaded part in the figure?
How many are there?
Wu Tong really didn't understand how a 28-year-old like her, who had been away from the classroom for ten years, could possibly remember the questions from high school.
Wu Tong frowned and rubbed her eyebrows in frustration. Who could have thought that when she woke up from her coma, she would be back to the summer vacation of her first year in high school and become a willful, ignorant and unmotivated poor student.
Her head hurt, and the scene of her father dying in a car accident and her mother in the emergency room, her life or death uncertain, appeared in her mind.
His heart felt like it was being pulled apart... The piercing pain made Wu Tong breathless.
The pen in his hand suddenly broke on the desk, and Wu Tong looked at the test paper in front of him.
There is still time for everything.
It's only 2009 now, she's only sixteen years old, and she's still preparing for the college entrance exam!
Wu Tong tried hard to concentrate, even half-heartedly thinking, if only there was something that could help her concentrate and get her mind focused!
Just when I was about to complain about my lack of concentration, I started dreaming before I even fell asleep!
Suddenly, a cool and peaceful feeling slowly spread from the depths of his mind, making Wu Tong feel as light and energetic as if he were eating a frozen watermelon in the dog days of summer.
In just a short while, Wu Tong had a vague clue about the problem that had been bothering her just now from her limited knowledge base. She had some ideas and it seemed that she could start with the intersection operation of the two sets M and N.
Is this a pie in the sky?
Or is it her illusion?
If it was an illusion, the idea of solving the problem that emerged in her mind was not false. This was a knowledge point that she could never remember now. The teacher had talked about it at that time, but she didn't listen carefully back then.
At this moment, she was completely focused. The knowledge points that she had only heard before were dug out in depth, connected from point to surface, and formed a way of solving the problem.
To describe it in one sentence, this is called the spark of inspiration.
If possible, Wu Tong certainly hopes that this is real and not a one-time occurrence.
In order to verify, Wu Tong carefully examined the question again, and the clarity of mind emerged again. All the distracting thoughts in his mind disappeared, leaving only the concentration on solving the problem carefully and following the previous train of thought.
The set shown in the shaded part of the figure is MnN···
∵M={x∈R|-2≤x-1≤2}={x∈R|-1≤x≤3}, and N={x|x=2k, k∈Z},
∴M∩N={0，2}
Therefore, there are 2 elements in the set shown by the shaded part.
After writing it down with great enthusiasm, the answer came to him, and Wu Tong really experienced the pleasure of doing the test.
If learning were so comfortable, then studying all the time would be a happy enjoyment rather than an anxious torture!
How many people desire to be able to write beautifully!
Wu Tong was pleasantly surprised by this unexpected encounter, but also curious about where this opportunity came from. Remembering that the magical feeling originated from deep within his mind, Wu Tong closed his eyes and concentrated his thoughts, carefully feeling the depths of his mind.
Her heart gradually calmed down. Suddenly, Wu Tong felt that her consciousness had suddenly come to a magical place. Her thoughts became clear and a wave of enlightenment came to her heart. This was the deepest part of her sea of consciousness. In it, a slightly damaged black jade stele stood quietly. Even though it was damaged, the jade stele still shone brightly and was moist and crystal clear.
Wu Tong's consciousness tentatively approached the jade stele, and she was enveloped by the jade stele's steady aura like a mountain. A warm current quietly flowed into her heart, and all the past and future consequences naturally emerged in Wu Tong's mind.
There exists a wondrous object in the universe known as the Enlightenment Stone, a naturally formed stele with the miraculous power of comprehending the ultimate truths of heaven and earth. However, time has passed, and today, the broken Enlightenment Stone's only remaining power is its meager ability to calm the mind and aid in the deduction of errors and omissions, and it is on the brink of extinction.
Today, it is activated by the energy of the intersection of time and space, and the owner Wu Tong accidentally awakens his past life memories, blends them with the future, and glimpses a hint of the future.
But for Wu Tong, these minor abilities are already extremely useful aids to her. It is her blessing to be able to obtain them. She is not greedy to reach the sky in one step and become an immortal or a Buddha.
All the tragedies started from her deliberate failure to study well after this summer vacation. Now, with the reminder of her past life memories and the help of the enlightenment tablet, the first step to change her destiny is to study hard.
Learning step by step and keeping her feet on the ground, acquiring more knowledge, becoming the pride of her parents, becoming a useful person, and being able to control her own life. This is the path that her parents are most satisfied with, and it is also the best path for her to develop.
In her previous life, she was tired of repetitive work and had no real understanding of the world. Although she knew that technology would develop by leaps and bounds in the future, she did not understand the principles behind it. She knew that housing prices in big cities would become higher and higher, but now she and her family did not have the money to buy a house in a big city.
Knowing someone will win the lottery, tens of millions or even hundreds of millions, so what? Her memory does not include lottery numbers.
Her family, like most others, lived in the ordinary little town of Xincheng County, Tianzhong City, in the Central Plains. Her father, Wu Jingzhong, was a civil servant working at the county agricultural bureau, and her mother, Jin Yu, was a primary school teacher, teaching mathematics. While the family wasn't wealthy, they could still provide for their basic needs.
She doesn't pursue extravagance and her financial situation isn't that bad, so she doesn't need to go out and earn money immediately to turn the tide.
There is a golden house in books. If you study hard, you can also make money.
She seemed to have heard in her previous life that a mathematician solved a mathematical conjecture and was rewarded with one million.
She didn't know her limits, but based on her personality, she was not good at socializing, and focusing on research-oriented work was the most suitable for her. Moreover, she now had the help of the Enlightenment Stone, so perhaps she could also strive for such glory!
Studying diligently, acquiring knowledge, and understanding knowledge can also become nutrients for the Enlightenment Stone, nourishing and repairing the Enlightenment Stone. They complement each other and make each other perfect.
In addition to the source, the Enlightenment Stone also gave Wu Tong a set of physical strengthening exercises, which Wu Tong named the Morning Sun Purple Qi Method. She used herself as a medium to absorb the purple qi from the rising sun every day, and combined it with special breathing to enter her limbs and bones, which could nourish every part of her body. Although it did not have the miraculous effect of changing one's fate, it could strengthen muscles and bones, enhance physical fitness, and prevent serious diseases.
Unfortunately, inhaling the morning glow purple energy was only suitable for her own use, as it was based on the coexistence of the enlightenment stone tablet with her. However, she had researched and simplified the breathing method, which she could pass on to her parents, along with gentle exercises to strengthen their bodies. With a healthy constitution, illness would naturally be less of a problem. They should at least strive for a long life of over a hundred years, without suffering any illness.
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