Breakfast, Beatrice, and Borel Sets

You wake and stare at the clock. It’s ten past ten. You scramble out of bed. Twenty minutes until class starts… you’ll have time to get changed and freshen up, but there definitely won’t be time for breakfast.

You silently chide yourself to not stay up so late, and then, nineteen minutes later, rush into class and find your seat by Helen, Mal, and Jack.

{if HelenAuctionDate == True} “Wow, I didn’t think last night would have taken that much out of you,” Helen says, raising an eyebrow in humour. {elseif MalAuctionDate == True} “A late night, huh?” Mal says, ribbing you. “Must have been some girl.” {else} “Had a rough night?” Mal laughs. {endif}

You look down at yourself and realize that only half your shirt is tucked in. Whoops. You pull it out, making a face.

“Was working on a writing seminar last night,” you groan. “Probably stayed up way too late… I don’t even know why, it’s due Friday.”

“That pretty much sums up me,” Helen laughs.

“Welcome, class,” Professor Ward says, walking into the classroom with a stack of tupperware in her arms. {if WardDetention2 == True} “Thanks to Alex’s efforts in ‘detention’ this weekend, we’ve got lemon bars for the class today! Help yourself to some, especially if you haven’t had breakfast…” Professor Ward catches your eye and smiles. {else} “I felt like baking last night, so I made some lemon bars for the class. Feel free to have some, especially if you haven’t had breakfast yet…” Professor Ward catches your eye knowingly. {endif}

Your classmates scramble out of their seats to get the lemon bars, and you join the queue, grateful for a chance to fill up your stomach.

The rest of the microeconomics class goes by quickly, and before you know it, you’re back out on the college quad, thinking about the latest math assignment. As you absent-mindedly wander towards the math building, a girl sitting on a nearby bench catches your attention, calling out your name.

“Hey Alex,” Beatrice says, dressed in a simple white t-shirt and jeans, wearing her brunette hair down. “Got any plans this afternoon?”

“What’s up?” you ask, shifting to the edge of the sidewalk, conscious of the students you might have been blocking.

“I was just thinking that we could work on the latest chemistry assignment together,” she says, giving you a hopeful smile.

“Yeah, what time?” you ask, pulling out your phone to check your calendar for the day.

“I could do 4 pm to 6?”

“I’ve got ‘Lab Research’ penned down for that time,” you say. “But, I could work on it some other time... Professor Styles seemed pretty flexible on the schedule when we talked. But, also, I don’t want to make a bad impression—this is my first week on the job, you know? Could you do anytime else?”

Beatrice shakes her head.

“That’s the only space I have today, unless you could do right now? I have a bit over an hour…”

“I was planning on going to office hours for math now,” you say.

“Oh um… no pressure! I’ll be working in the library now and then later too, so I’ll text you the spot, and then you can decide whether to show up or not?”

“I’ll let you know,” you smile.

“Catch you later then,” Beatrice says. “Or, um… maybe not?”

Professor Luck’s door is still closed when you get there.

“Hey hey, Alex,” Ruby says. {if Calc1Ruby == True} “Any reason you wanted to meet at Luck’s today?” {else} “Didn’t think I’d catch you here today!” {endif}

“Yeah, I had a couple questions about Borel Sets that I wanted to run by Luck,” you say. “I think I get the concept, but there’s some trickiness in the latest problem set…”

“Oh yeah, I took a look at those problems too, they seemed pretty hard,” Ruby says.

The door suddenly bursts open and a jacked grad student lumbers out, rubbing his hand through the back of his prickly hair.

“So go talk to the department chair, if things still aren’t sorted out in a week, let me know,” Professor Luck says.

The grad student nods thankfully, and then makes his leave.

Professor Luck turns to look at you and Ruby.

{if Luck > 0} {if Calc1Ruby == True} “Ruby and I have been working together a bit, but we ran into something tricky on the Borel Set questions that we’d like to ask you about,” you say. {else} “I had a question about Borel Sets, and thought it would be good to talk it over with you,” you say. {endif}{else} “What are you doing here, Alex? I thought I told you not to come back.” {endif}

{if Luck < 1} “Uh… right,” you say, embarrassed by your feeble attempt to get physical with Professor Luck last time you had office hours with her. “Hey, um, Ruby, let’s go somewhere else to work?” {endif}

{If Luck > 0} “Okay! Why don’t you head on in?” Professor Luck says, welcoming you into her office. “I’ve already gotten an email or two from others in the class about Borel Sets, so I’m thinking that I must not have explained them terribly well. Would it help if I covered that again?”

You and Ruby glance at each other, and then nod.

“So the definition of a Borel Set isn’t very tricky to grasp, I think,” she says, erasing a section of her blackboard. “It’s just any set that can be formed from countable unions, intersections, and complements of open sets—that makes sense, yes? Right. And then the Borel algebra is just a sigma algebra, which we defined as…”

Professor Luck quickly covers the intuition behind the math and goes over some basic properties, most of which you got the first time in class, but still—it’s nice to have a refresher. She wraps up soon enough, and looks back at the two of you questioningly.

“So that’s all you really need to complete the assignment,” she says. “Any other questions?”

“That was great, thank you!” Ruby pipes up. She closes her notebook and gets up to leave, and then she pauses by the doorway. “You want to come with me to work on the problem set, Alex?”

“You’re also welcome to stay and work here if you want,” Professor Luck says with a warm smile. “It is still office hours.”

“It gets a bit cramped in here, I feel like I think better in the library,” Ruby says.

There’s a pause in the air, and you realise that both women are looking at you. Right. Looks like you have to make a decision again.

You could leave with Ruby and work through the problems with her—you did tell Vignesh that you were going to help him get her, and you have some murky sense that this might help, somehow. On the other hand, Professor Luck is much more likely to be helpful, and, you can’t help but think to yourself, if the two of you are alone in her office, well… things could happen.

Then, there’s Beatrice, too. You could go work on chemistry with her, and that would mean that you could go to lab later, guilt free.

Choices, choices...{endif}

Ruby +5
Luck +5