One fine evening, many days later, Lexus was sitting at his desk in his room, reading through "Discrete Mathematics" with pen and paper in hand. Although this was no different from any other day of his life, Lexus felt unusual excitement as he turned page after page, deliberately making connections to his preexisting knowledge.

He had purposefully chosen to stay in his room that evening, as opposed to the college library where he typically studied. Arthur gave Lexus a strange look when Lexus said he wasn't going, but didn't probe any further, instead leaving to find the rest of their course mates who also happened to be studying in the library.

Lexus had something else to do though.

He was waiting. Waiting for that sound...

Ding!

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Mathematics EXP +1

Mathematics levelled up from Level 0 to Level 1. Congratulations!

---

"Yes!!"

Lexus instantly leaped out of his chair and crashed onto his bed on the other side of the room, rolling around and making a mess of his bedsheets along the way. He was kicking and thrashing all over the place, and if anyone were to enter into his room at that moment, the only explanation Lexus could give would be "there is a fine line between genius and insanity".

A full five minutes later, Lexus was so physically exhausted that he could do nothing more than lie on the top of his bed, breathing heavily. The system, who seemingly waited for Lexus to calm down or tire himself out trying to do so, spoke at that moment.

"Congratulations, Lexus. You worked hard."

Lexus felt a warm, fuzzy feeling in his heart from the system's rare compliment. Other than himself, the system was the only entity that could tangibly see his progress, so getting recognition from it meant a lot to him. He had gotten so used to the system's bashing and mocking that genuine approval felt unusually hard-earned.

Ding!

Huh?

Lexus was initially confused, but confusion was quickly replace with excitement when he saw the words on the screen.

---

Feature unlocked [Mathematics]: Right or Wrong

---

Ooooooh!

"System, what is this?"

"Don't be so impatient," the system replied.

A pause. Lexus waited, patiently, for the system to continue.

"Want to guess?"

"Argggh!" Lexus said. "Please, just tell me!"

The system sounded amused when it said, "See, way too impatient."

=====

After a few rounds of explanations, questions and then more explanations, Lexus gathered from the system that the new feature introduced allowed him to determine whether his answer to a given mathematics question was right or wrong.

What it didn't allow him to do was give him hints as to how to solve the problem, so he would still have to figure out everything by himself. If his answer to the question was wrong, the feature also wouldn't be able to point out where exactly he went wrong, he would just know that it was wrong.

It reminded Lexus of his experiences when programming: despite the computer's best efforts to tell him what was wrong with his code, the error messages were always vague at best, indecipherable at worst. So it was often up to him to comb through his code line by line in a frustrating attempt to figure out the mistake.

Despite its limitations, Lexus was very excited about this feature. Why?

Because it meant no careless mistakes, no false logic, no thinking that he was right when he wasn't. When the answer was correct, it also meant that he knew that it was right, with full confidence. If he had this during his A Levels, he would have scored full marks in maths, no problem.

To Lexus, it was like to having his paper marked while he was in the middle of completing it. What more could he have asked for?

Lexus decided to put this feature to the test.

There were a few things he wanted to see:

1. Whether the feature worked like it said it would, for both right and wrong answers to calculation questions

2. Whether the feature would work for proof questions

3. Whether the feature would work on other people's work

He was particularly excited for the last one, but the first thing to test was whether feature actually worked like the system said it would.

Lexus flipped back to one of the earlier chapters of "Discrete Mathematics" and picked a question that he had done before and checked the answers for.

In each of the following cases say whether or not the set X has a lower bound, and if it has a lower bound, find its least member.

i) X = {x ∈ ℤ | x2<=16}

ii) X = {x ∈ ℤ}|x=2y for some y ∈ ℤ}

iii) X = {x ∈ ℤ|x2<=100x}

Lexus scribbled down:

i) yes, least member = -4

ii) no

iii) yes, least member = 0

He finished writing his solution down and waited for something to happen.

A tiny notification window popped up next to his working, with a single word:

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Correct

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Lexus wasn't surprised that he got the question right, but he was still very happy to see the message pop up in front of him. This particular question was an easy one and Lexus could have easily double checked it himself, but the feature would come in very handy for calculation intensive questions which were difficult to verify.

Next, Lexus wanted to see if wrong answers would get picked out.

This was relatively easy to check, Lexus just changed the -4 from his previous working to something else, like 2, saw the window almost instantly change.

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Wrong

---

Nice.

Lexus changed his answer back to make the "Wrong" go away, and moved on to testing the second query he had: to see if the feature would work on proofs.

Lexus decided to try it out on a simple proof by induction question:

Use the principle of induction to prove that 12 + 22 + · · · + n2 = 1/6 n(n + 1)(2n + 1)

It was a fairly standard proof, and Lexus completed it without much trouble. Prove the base case, prove the inductive step, tie it all together. Let P(n) be the statement that 12 + 22 + · · · + n2 = 1/6 n(n + 1)(2n + 1)

Base case: when n = 1, 12 = 1 1/6 (1)(2)(3) = 1 Therefore the base case is true. Inductive step: Assume P(k) is true for some k ∈ ℕ, i.e. 12 + 22 + · · · + k2 = 1/6 k(k + 1)(2k + 1) Then

12 + 22 + · · · + k2 + (k + 1)2 = 1/6 k(k + 1)(2k + 1) + (k + 1)2

= 1/6 k(k + 1)(2k + 1) + 1/6 (6k + 6)(k + 1)

= 1/6 (k + 1)(2k2 + k + 6k + 6)

= 1/6 (k + 1)(2k2 + 7k + 6)

= 1/6 (k + 1)(k + 2)(2k + 3) Hence P(k) is true ⇒ P(k+1) is true.

By induction, 12 + 22 + · · · + n2 = 1/6 n(n + 1)(2n + 1) for all positive integers n.

---

Correct

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The last thing Lexus wanted to check was whether the system could tell whether answers from other people were right or wrong. This was easy to check: Lexus simply flipped to a random page on "Discrete Mathematics", looked at one of the worked examples, and waited for the system to do something.

---

Correct

---

Lexus was amazed. "System, can you read my mind?"

"No, at least not at this stage. It's obvious enough what you want me to do though, especially when you're just sitting there like an idiot, doing nothing but stare at the symbols," the system replied.

Lexus was in a good mood at the moment, so he decided to forgive the system's snarky antics. "System, can you leave this feature on every time I work on a question?"

"Yes, that is possible," the system replied.

Lexus tested the feature on a few more questions, working on a problem sheet for his digital electronics module due a few days later. He hadn't yet come across a question in which the feature didn't work. Be it calculations, proofs, or even diagrams, as long as there was a right answer and a wrong answer, the system could tell him whether his work was right or wrong.

There were a few problems on the problem sheet that the system told him was wrong, and initially Lexus thought the system was talking crap. However, in every case it only took a few seconds of looking over the working closely to discover the mistakes, and after a few of these experiences Lexus came to trust the system more than his own intuition.

Lexus was starting to realise how overpowered this feature was. It only gave him one piece of information, a single word, but it meant so much more. He no longer had to hope for the best and instead could be certain about his work. Well, perhaps he would be certain that he was wrong, but he would rather know the cold hard truth than live in blissful ignorance.

At his current stage though, he couldn't do much more with the feature than to double check his work when attempting textbook exercises or problem sheets.

And it also didn't help if Lexus couldn't figure out how to do the question. He didn't need the system's notifications to know that he was wrong, and no amount of "this is wrong" would get him any closer to solving the actual problem. Lexus knew full well that this wasn't something a level 1 feature could possible do though, so he wasn't bummed out at the fact that this pipe dream didn't come true.

Having tested the new feature to his heart's content, Lexus returned to continuing with his work, completing his problem sheets and programming tasks for university before moving on to make some progress with the reading quest.

=====

"System, status!"

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Name: Lexus Kagan

Current Quest: Background Knowledge [6/10]

Computer Science: Level 0 [EXP 30/100 (30%)]

Mathematics: Level 1 [EXP 94/1000 (9%)]

Physics: Level 0 [EXP 0/100 (0%)]

Engineering: Level 0 [EXP 0/100 (0%)]

Chemistry: Level 0 [EXP 0/100 (0%)]

Biology: Level 0 [EXP 0/100 (0%)]

---

Lexus looked at his screen, and sighed.

It had been over two weeks since his mathematics levelled up, and Lexus had made some progress with the quest, completing the 6 mathematics textbooks on the quest list. He hadn't expected the required experience to multiply directly to 1000 EXP points though. Seriously. 1000! It had taken him forever just to level up from 0 to 1, and at the rate he was going, he wasn't going to level up mathematics again any time soon.

On the other hand, his computer science progress looked more promising.

Lexus pulled out the list of 10 books that the system had tasked him to read, and made a note of the remaining books he had to read:

1. Cormen, T.H., Leiserson, C.D., Rivest, R.L. and Stein, C. (2009). Introduction to Algorithms

2. Kleinberg, J. and Tardos, É. (2006). Algorithm design

3. Sipser, M. (2012). Introduction to the Theory of Computation

4. Russell, S.J. and Norvig, P. (2010). Artificial Intelligence: A Modern Approach

The remaining books, according to Lexus' understanding, were all directly related to computer science, so Lexus expected to start gaining computer science experience soon. His current 30 experience points in computer science were entirely from the quest bonuses, which was why his mathematics level was so far ahead of his computer science level.

However, that was going to change soon.

"System, I'm going to get computer science experience out of these right?" Lexus asked.

"Mostly, yes," the system replied.

"Great!"

Lexus was excited. He didn't know what he would do if the system said "no", because 4 books wasn't nearly enough to push his mathematics level from 1 to 2. However, it was more than enough to level up his computer science, so Lexus was very motivated to finish the quest once and for all. Off to the college library it was!