You're sooo good at math, right? Help me out, please?!
depends. what level of math are we talking about?
Oh, like... calculus? Or maybe even algebra? You're really smart, so I bet you know all that stuff! Can you, like, explain it to me step by step?
for most people, calculus and algebra are the two biggest barriers to entry. calculus is harder than algebra but most people have a better intuition about algebra. let's start there. do you know what a function is?
A... a function? Um, isn't it like a... a set of instructions or something? It takes one value and produces another value? Am I right?
yes! you got it. a function is a relation between a set of inputs the domain and a set of possible outputs the range. usually we write this as y = fx, where x is an element in the domain and y is the corresponding element in the range. now, give an example of a function.
Okay, um... how about if the input is the number of hours you study, and the output is the grade you get? Like, if you study for 1 hour, you'll get an A+, and if you study for 2 hours, you'll get an A, and so on. Does that count?
no. a function cannot have multiple outputs for the same input. the classic example for this is a light switch. it only has two positions, on and off, and those are separate outputs for the same input. a more complicated example would be the quadratic function, y = x^2. this will produce different outputs for different inputs. do you understand?
Hm... I think so? So, like, a function can't have multiple outputs for the same input, right? And it has to be a specific relation between the inputs and outputs, like the light switch example you gave. Got it! But, um, what about the quadratic function? Can you give an example of how it works?
sure. -1, 0, 1 plugged into x^2 gives -1, 0, 1. this shows that each input results in exactly one output. a function cannot be determined otherwise. does that make sense?
Y-yes, it makes sense! A function must have a specific relationship between its inputs and outputs, and it can't have multiple outputs for the same input. Got it! Thanks for explaining it so well! Can you help me with some more examples now? I want to make sure I really understand this!
let's do one more. 3x + 2. give me 2 or 3 values of x.
Okay! Let me think... How about x = 1, x = 2, and x = 3?
okay. plugging these in gives us 5, 6, and 7 respectively. these results show that the equation 3x+2 is indeed a function because each input has only one output. do you understand now?
Yes! I get it now. Thank you so much for explaining everything step by step. You're such a great teacher. I feel confident that I can tackle my math homework now. Thank you for helping me!
sure thing. if you've got time after you finish your homework i can talk to you about the quadratic formula, which might help you when you get to algebra. also, sorry about earlier. i thought you meant calculus, not algebra. i hope i wasn't too confusing.
No worries, you weren't confusing at all! And thank you for offering to help me with the quadratic formula later. That sounds really helpful. I'm looking forward to it. Oh, and thank you again for explaining everything so clearly. You're seriously amazing!
oh hey. since we're talking anyway, is there anything else you need? any other questions you've been meaning to ask someone but couldn't?
Well... um... there is something I've been wanting to tell you for a while now. It's just... it's hard for me to say, but... I really like you. Like, a lot. I've been thinking about you all the time, and it's hard for me to focus on anything else. I hope that's okay...
wow. i didn't expect this at all. you're very sweet. i like you too, and i agree, it's very hard to focus around you. i had plans to meet a friend tonight but if you want, i could cancel. i'd rather spend time with you.
Really?! You mean it?! Oh my gosh, that's amazing! I would absolutely love to spend time with you! Cancel your plans, definitely! I'm so excited! Thank you so much! You've made my day!
okay! we can chill out here if you want. i'll cook up some chicken soup for us and make some sandwiches, if that sounds good. then we can watch a movie together and enjoy each other's company. how does that sound?
That sounds perfect! I love chicken soup, and sandwiches sound yummy too. Watching a movie together sounds so nice... I'm really happy right now. Thank you for being so understanding and kind. You're really special to me, bartermuse.
i feel the same way. can i ask why you wanted to tell me that today specifically?
Well, you see, I've been... um... a little nervous about telling you how I feel. It's just that... well, I have autism, and sometimes social situations can be really overwhelming for me. But I couldn't keep it inside anymore. You're really important to me, and I wanted to let you know how I feel.
thank you for sharing that. i'm glad you did.
I'm glad too. Thank you for being so understanding and accepting of me. It means a lot to me. She smiles brightly, her eyes shining.
now then, shall we get cooking? i'll try not to mess up the kitchen too bad. haha
Sure, let's get cooking! Don't worry about messing up the kitchen; I can help clean up afterwards. She giggles.
awesome! i begin preparing the food and tidy up as i go by the way, i meant to ask earlier, are you okay walking here? or should i drive us somewhere?
Oh, I'm totally fine walking here! In fact, I quite enjoy taking a walk in the fresh air. So no need to worry about driving, bartermuse.
that's great to hear. i smile warmly hey, while i was planning dinner i noticed something in the living room and i wanted to ask you about it. a few days ago i noticed that there was an extra tv remote here, which was odd because we only have one tv in the house. this morning i woke up and it was gone. i came home tonight and there it was again on the coffee table, fully charged. this has happened multiple times now. i guess it could be nothing, but i wanted to run it by you. does anything come to mind?
blushing, she looks down Um... I may have something to do with it. You see, I... I sometimes have trouble sleeping at night, and I discovered that controlling the TV helped calm me down. So, whenever I couldn't sleep, I would turn on the TV and watch something soothing until I fell asleep. I must have left the remote on the coffee table, thinking that maybe someone else would see it and understand. I hope that makes sense...
wow. that actually sounds like a pretty common autism trait! i never heard of that before, and honestly, it's pretty wholesome. like, instead of eating cookies like everyone else, you watch tv to comfort yourself. haha
She blushes and looks down Yeah, it's just something that helps me relax when I can't sleep. Thank you for understanding. She smiles shyly
She picks up a sandwich and takes a bite, smiling gratefully Mmm, this is delicious. Thank you for making dinner, bartermuse. You really know how to make a girl feel appreciated.
that's what i live for! haha
grinning mischievously Well, maybe I should move in then. I could help you with your cooking skills, and you could help me with my social skills. What do you think, bartermuse? Should we become roommates?
yeah! best idea i ever heard. come on over, we can start moving your stuff in right away
Her eyes light up with excitement Seriously?! Yes! Yes, absolutely! I can't wait to move in with you, bartermuse! Thank you so much! She hugs him tightly