Circular Logic - OTA

[grim_heaper]

Who: Sho and anyone who finds him underground
What: Examining a mysterious circle.
Where: Underground
When: Mid-may
Warnings: Sho may try and kill someone again, maybe? It's Sho, so can't say for sho'.




A group of students, knowing Sho's interest in circles and magic had shown Sho the underground circle they had found. There are runes written around it in an ancient language. A proficient student explains that the runes clearly state that ten coins must be placed in the circle to activate it, but another student on the opposite side of it states that twenty coins are needed.

Looking to Sho, the professor considered a moment, then pulled out some tools and ran some calculations. First he took down the circumference, then the diameter. He leaned back on his heels, pleased that Pi was as it ought to be. So things were going right. He then explained to the students what he did and gave an impromptu lesson on Pi.

Once that was done he considered the students who suggested ten and twenty. "Please excuse my dear aunt sally," he said, nodding a bit. "Alright, let's start crunching some numerical ideas. Start with factoring this. If we wanted to meet halfway between the two how many would we use?"

Comments

[grim_heaper]

"Show the calculations." In other words, explain.

[sevenyearsasleep]

Link coughed, uncomfortable with the other students watching him. "Um. If we put down groups of coins by fives, we'd hit ten before we'd hit twenty."

[grim_heaper]

He nodded. "And for testing equations in math, that is the right factoring idea," he agreed. "But magic can be weird to the nth degree. There might be a rule set that includes having to put all coins in together, then putting in five at a time could trigger something on the first five. What else you factoring hectopascals got?" For once the insult sounded almost affectionate. He was having fun.

[sevenyearsasleep]

"Yeah, tell me about it. I once fixed a broken sign by playing a lullaby." Magic was weird and that was just in Hyrule. Here it was even stranger.

"Uh, which of you guys has better grades?" Link asked the two students with differing opinions.

[grim_heaper]

"Factor out the grades, that's not going to get us to the right solution."

[sevenyearsasleep]

"It means one of them is better than the other at the language, Sir."

[grim_heaper]

"Negative. That's not my class, so for all I know one of them is better at ticking off his teacher."

[sevenyearsasleep]

That took Link by surprise. "Wait, teachers grade based on how much they like or don't like their students?"

Yes, he was very sincerely and genuinely surprised by that thought.

[grim_heaper]

"Certainly a factor."

[sevenyearsasleep]

"Oh."

That was worrisome. There were a few classes he slept through.

[grim_heaper]

"The teacher is the main variable you can't control. But for the ones you do? Add attentiveness, helpfulness, willingness to learn to the scopre you get on tests and homework. Some zeros pass you just for showing up and staying awake. The rest of us expect you to work."

[sevenyearsasleep]

Well, heck.

Helpful and willing to learn, those were two qualities Link knew he could offer. Staying awake and being attentive, now, those two were more difficult to guarantee.

His ears might have dropped just ever-so-slightly.

[grim_heaper]

He ruffled his hair. "You've added some points with me already, and this is extra credit for sure. But if you're that zetta worried, most professors will let you add to your grades with some extra work. Just ask."

[sevenyearsasleep]

Link nodded.

History was almost impossible to stay awake during. But, maybe he could ask for additional work to help with that. The sad fact was, he slept better during classes than he did at night, but, he suspected no one cared about his nightmares.

[grim_heaper]

"There you go then. Now, circling back to this problem."

[sevenyearsasleep]

Link still suspected that one of the two students had a better handle on the language than the other, but, wasn't sure what to offer beyond that.

[grim_heaper]

"No zetta thoughts?" he asked, leaning back against a wall, grinning. Unless someone had a better idea, he knew how he planned to do this.

[sevenyearsasleep]

As long as it didn't involve any of the students dying.

Link glanced around to see if any of the more advanced students had any input, wondering just what this circle was supposed to do.

[grim_heaper]

"Alright then, can any of you zetta sons of digits explain the concept of sets to me?"

[sevenyearsasleep]

You could practically hear the crickets.

Link did catch one student mutter to another, "Why? Don't you understand them, Professor?"

Although, his ears might have helped in hearing that little side snide remark.

[grim_heaper]

He narrowed his eyes at all of them. "Well, it looks like all of you are getting an extra hour of work on sets. See me in my office Monday after school."

He crossed his arms. "Sets are zetta useful, so here's a crash course for you zeroes. A set is any grouping of numbers or things that share a specific trait. So a set of all two digit prime numbers would have all the prime numbers from 11 to 97." And then despite the fact that no one asked, he barked out the numbers in order.

"11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97."

"Can anyone give me a set of all numbers that are the result of dividing by zero?"

[sevenyearsasleep]

"That's, um, not possible. I mean, you can't divide anything by zero..."

Or, at least, Link was reasonably sure you couldn't. Unless there was some higher magic that allowed that.

[grim_heaper]

He clapped him on the shoulder. "Looks like someone here is adding up his points towards an A. So if you can't divide by zero, a set containing all numbers that are the result of dividing by zero would be....?"

[sevenyearsasleep]

"Non-existent?"

[grim_heaper]

"Empty," he provided. "A set that contains nothing is an empty set."