Chapter 2
Unable to calm down due to her excitement, Ji Zhixing first chose the physical training task under the "Integration Power" list and ran wildly on the playground under the midday sun.
Due to long-term malnutrition and insufficient rest, Ji Zhixing's physical condition wasn't very good. But today, his inner restlessness drove him to run several laps without getting tired. Only when the system called a stop based on his physical condition did he stop and walk along the edge of the track, adjusting his breathing and relaxing his tense leg muscles after exercise.
[Complete today's "Integration Power" "Physical Training" task, +1 point]
Upon hearing the system notification, Ji Zhixing couldn't help but laugh. Looking at the dazzling, blinding sun overhead, he felt as if his entire life had been illuminated.
Ji Zhixing returned to his dorm and took a quick shower. After completing an easy task, he decided to alternate between easier and more challenging ones, starting with the seemingly more difficult "creativity" task. He then received this problem:
Please prove that the infinitely repeating decimal 0.999... = 1
Huh? This...
Ji Zhixing copied the problem onto a piece of draft paper, picked up his pen, and began to think about it.
Elementary school students all know that 0.999… is “approximately equal to” 1 and is naturally less than 1, but this question requires proof that they are “equal to”. However, since this is a question designed to develop creativity, the requirement is not to prove that the two are objectively and irrefutably equal, but rather to broaden his creative thinking and enable him to find alternative ways to equate the two.
Ji Zhixing pondered for a moment, deciding to start with the number 0.999...
0.999……=9/10+9/100+9/1000...
He pondered the broken-down formula for a long time, but couldn't figure out how to use it.
Okay, let's try a different approach.
Geometric series, if r < 1... won't work!
If we use real analysis to give a set of nested intervals, 0.999... corresponds to the nested intervals [0,1], [0.9,1]...[0.999,1]... but that doesn't work!
Ji Zhixing scribbled various mathematical formulas and theorems on the draft paper.
Dedekind split...
Cauchy sequence...
He tried to calculate again and again using various formulas and theorems, but the equations became more and more complex and the numbers became larger and larger. After writing more than a dozen sheets of draft paper, he still couldn't figure it out. So he started to try setting X.
X=0.999……
Well, the key is the infinitely repeating last digit. If we can subtract the last digit, the equation will be much simpler.
Try moving up one more position...
10X = 9.99...
10X - X = 9.99... - 0.999...
The last few digits have been reduced!
9 x = 9!
X=1!
It's out!
If X=1, and we previously set X=0.999..., we can prove that 0.999...=1!
Ji Zhixing slammed his hand on the table. He had overcomplicated things. There was no need for those mathematical formulas at all. In fact, as long as the approach was right, even a middle school student could solve this problem.
Ji Zhixing earned another point from this question. In total, he earned 2 points in just over an hour, netting 200 points – more than his hourly tutoring wage! It was effortless, improved his learning ability, and saved him time commuting.
Ji Zhixing stared at the small number 2, looking at it with satisfaction for several minutes.
With three of the five task branches remaining, Ji Zhixing considered for a moment and decided to complete the "Reading Professional Books" task under "Comprehension" first. He would go to the library to read the textbooks for next semester and also preview his lessons.
During his freshman year, he had to spend time and energy working part-time, so his grades were just average. Now that he has a stable source of income, he feels he can look forward to the scholarship next semester.
After helping Ji Zhixing familiarize himself with the basic tasks, the system entered a non-disruptive mode. Ji Zhixing continued to study and practice day after day, and a month quickly passed. With only a week left before the start of the semester, many postgraduate entrance exam candidates took short breaks to relax, and the library became emptier each day. However, Ji Zhixing still arrived at the library on time every day.
This month, he finished reading all the textbooks required for second-year students, including "Mathematical Methods in Physics (A)," "Physics Experiments," "Optics," "Atomic Physics," and "Theoretical Mechanics." While there were many obscure and difficult parts, Ji Zhixing persevered and gained a lot—both knowledge and money. As for the parts he couldn't understand in the textbooks, he'd leave them for the classroom after the semester started.
His goal today is "Engineering Graphics". After finishing this book, he will have gone through all the textbooks he will need in his second year of university.
However, Ji Zhixing was unable to fully concentrate on his books all day.
This month, he developed a good habit of reading every day, and thanks to his daily 30-minute meditation practice, he has been able to quickly enter a reading state. However, perhaps because of meditation, his perception of the outside world is also more acute than before, and today he felt as if someone was subtly watching him.
Looking around several times but finding nothing amiss, Ji Zhixing decided to ignore it. Studying was the priority, but accumulating points was even more important. He had already accumulated over a hundred points, and with the start of the semester approaching, he exchanged them for 4,500 yuan to pay for tuition and accommodation. He had no outstanding debts, and with nearly a hundred points remaining in the system, he felt an unprecedented sense of ease and peace of mind.
After completing his studies at the library, Ji Zhixing returned to his dormitory and saw his roommate Xu Dongyang as soon as he opened the door.
As soon as Xu Dongyang saw Ji Zhixing, he closed his laptop: "You're finally back! Hurry up! I've been waiting for you for ages." As he spoke, he slapped open several insulated food containers on the table.
As soon as the lid was opened, the aroma of the food wafted into Ji Zhixing's nose, making his stomach rumble.
The insulated box was filled with crispy pork, braised pork ribs, fried chicken wings, and other meat dishes. The glistening oil made Ji Zhixing's mouth water.
Actually, since he started earning points through the system, Ji Zhixing's meals weren't too bad. Although he still ate all three meals in the cafeteria, he was now willing to order proper dishes with both meat and vegetables for himself. However, the cafeteria food was definitely far inferior to Xu's mother's cooking in terms of taste.
"Are you going to work again later?" Seeing Ji Zhixing shake his head, Xu Dongyang opened two more cans of beer.
Ji Zhixing didn't refuse. He put down his backpack, took the beer and chopsticks, and sat down to eat. After a bite of crispy-on-the-outside, tender-on-the-inside fried pork, Ji Zhixing's parched stomach felt as if it had been nourished by the Niagara Falls; every pore screamed with satisfaction. Xu's mother's cooking was still as good as ever!
Xu Dongyang is a local resident who often goes home and always brings back delicious dishes cooked by his mother when he returns to school.
Ji Zhixing knew that Xu Dongyang couldn't bear to see him eating only steamed buns and vegetables every day, so he was supplementing his nutrition in this way. He felt that he was able to maintain basic health last semester and not collapse due to malnutrition, which was largely due to Xu Dongyang's occasional feeding.
The two ate and chatted.
Xu Dongyang asked, "Did you go to the library this morning?" He had just seen him come back with a backpack full of books.
"Yes, I've finished previewing all the books for this semester," Ji Zhixing said proudly.
"Wow! Then I'll be counting on you this semester." Although Xu Dongyang didn't fail any courses last semester, he barely passed two of them, and this semester's courses will only be more difficult.
Ji Zhixing smiled and agreed. In the past, he wouldn't have dared to say how much he could help Xu Dongyang academically, because he used to spend most of his free time working and didn't have much time to study. However, things were different now. After focusing on his studies for a month, and knowing he could continue to do so, he was very confident about his grades this semester.
Xu Dongyang then noticed that Ji Zhixing was a little different: "Damn, I didn't even look closely. He's completely different after just one month."
Although Ji Zhixing used to have handsome features, he was too thin, sometimes to the point of being unrecognizable. But now, Ji Zhixing's cheeks are fuller, and although he is still slender, he is not weak and looks very energetic. He is full of vitality and looks brighter.
He knew that Ji Zhixing was working on campus during the summer vacation. During that time, he called several times to invite Ji Zhixing to his house for a meal, but Ji Zhixing refused to go. He was worried that one day Ji Zhixing would suddenly collapse in the dormitory or on the way to work due to malnutrition. He originally thought that he would see Ji Zhixing today, who was tired and tanned after two months of hard work, but he did not expect that he would be fair-skinned and strong instead.
Just as I was about to ask more questions, the dormitory door was suddenly banged on loudly.
"Open the door! Ji Zhixing, I know you're inside!"
Who is this? Xu Dongyang looked at Ji Zhixing in confusion. Ji Zhixing didn't recognize the voice either, but he still got up to open the door. Xu Dongyang also put down his chopsticks and followed closely behind him.
As soon as the doorknob was turned, someone burst in, crashing through the door—it was Liu Shihui, a classmate. Counselor Chen Yan followed a step later.
As soon as Liu Shihui entered the room, he pointed at Ji Zhixing and angrily shouted, "Director Chen, it was him! He stole my watch!"
Ji Zhixing frowned, slapped his hand away, and said to Chen Yan, "Director Chen, he's spouting nonsense! I've never even seen his watch!" Is he having a run of bad luck with watches lately? One after another!
“I saw it with my own eyes, how could I be wrong?” Liu Shihui said, glancing around. He pointed at the backpack on the table and said, “It’s this backpack. I saw you hide the watch in it with my own eyes in the library.”
Ji Zhixing's heart sank. Of course, he knew he hadn't stolen the watch. But Liu Shihui had spoken so confidently, so there was probably a watch that had mysteriously appeared in his backpack.
He suddenly remembered the strange feeling he had experienced in the library that morning. Now that he thought about it, Liu Shihui might have been the one watching him there. He guessed that when he went to get his water bottle, Liu Shihui had tampered with his backpack.
Seeing that Ji Zhixing didn't speak for a moment, Liu Shihui rushed over, grabbed the backpack, unzipped it, and started rummaging through it.
Ji Zhixing didn't stop him; any attempt to obstruct him at this time would only increase his suspicion. So, unsurprisingly, he saw Liu Shihui pull a watch out of his bag.
“Look! Isn’t this it!” Liu Shihui walked up to Chen Yan with the watch in his hand. “Director Chen, look, I didn’t wrong him.”
The commotion from knocking on the door had already attracted the attention of many people. People on the same floor gradually gathered at the entrance of dormitory 310 to watch the excitement. When they saw that Liu Shihui had actually found the watch, they couldn't help but murmur and whisper among themselves.
"I didn't realize that. I thought he was really poor but had a lot of pride."
"Could it be a misunderstanding? I don't think he's that kind of person."
"There's solid evidence, yet you still misunderstand."
Someone craned their neck to take a look: "Damn! It's a Rolex Submariner!"
"Zhang Biao, how much is this?"
"It depends on the specific model. The lowest price in this series is 50,000, and there are also some that cost over 300,000."
Wow!
Hearing a gasp behind him, Liu Shihui felt a surge of pride and said loudly, "I lost my watch in the library this morning. I was looking for it when I saw Ji Zhixing stuff a watch into his bag. I wasn't sure if it was mine, so I didn't say anything. But then I thought, how could a penniless guy like him afford a Rolex?"
Then, with a veiled threat, he said to Ji Zhixing, "If you ask me, you'd better stop being stubborn. Otherwise, this watch, worth over 100,000 yuan, is enough to keep you in jail for several years and get you expelled from school!"
Seeing Ji Zhixing remain silent, Liu Shihui felt a surge of satisfaction. Serves him right! Who told you not to let me cheat on the final exam last semester? We sat so close, yet you showed no classmate affection whatsoever, causing him to fail three subjects.
Although the evidence seemed conclusive, Chen Yan did not jump to conclusions. He looked at Ji Zhixing and asked, "Zhixing, do you have anything to say?"
Xu Dongyang spoke first: "Director Chen, Zhixing is definitely not that kind of person!" Having shared a dorm room for a year, he had complete faith in Ji Zhixing's character. Moreover, he always felt that Liu Shihui's reaction was a bit strange, as if his anger was somewhat fake.
Ji Zhixing had just thought it through carefully. The place where he sat in the morning was a blind spot for surveillance cameras, and when he went to get water it was close to noon, and there were hardly any people around, so it would probably be difficult to find eyewitnesses.
He thought for a moment and said to Chen Yan, "I didn't steal the watch, I didn't even touch it. You can call the police to check the fingerprints on it, they definitely won't be mine."
"Nonsense, you must have wiped it off beforehand!" Liu Shihui shouted. "You even broke it! Look at this huge crack on the dial, the hands aren't moving at all. But, for the sake of our classmate relationship, you pay me back the original price, and I won't hold you responsible."
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