http://charlieeppes.livejournal.com/ ([identity profile] charlieeppes.livejournal.com) wrote in [community profile] fandomhigh2005-10-21 03:01 pm
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MATHS CLASSES: Friday 21.10

Charlie's desk is overflowing with papers today, and two of the blackboards are covered with x, y, brackets, equal signs and exclaimation points. Charlie seems a little frustrated but mostly cheerful. He tells you that he's moved his office hours to Tuesdays, and that four consecutive classes missed without an excuse now equals being kicked out of class. He then gives you a sheet of paper and tell you to go sit down.
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Re: Advanced

[identity profile] miss-thomasina.livejournal.com 2005-10-21 03:08 pm (UTC)(link)
Thomasina has to think for a moment before remembering this one, but when she answers, it is with completel confidence. e's irrationality can be demonstrated through a proof based on its series expansion. If one supposes that e=a/b, and that a and b are positive integers, one can then demonstrate that for the number x=b!(e - Σ 1/n!) [b, n=0] x is not only an integer, but a positive integer that is less than 1. Since there are no positive integers less than 1, e is, of necessity, irrational.

[OOC: Please forgive my bastardised notation. The b obviously belongs over the Σ and the n=0 below it.]

Re: Advanced

[identity profile] charlieeppes.livejournal.com 2005-10-21 03:14 pm (UTC)(link)
"Excellent, Thomasina!" Charlie smiles.


((ooc: dude, like I'd know. *g*))

Re: Advanced

[identity profile] miss-thomasina.livejournal.com 2005-10-21 03:25 pm (UTC)(link)
Thomasina smiles back, quite cheerfully. Thank you. That one's quite simple to prove - unlike Fermat's joke.

[OOC: Yeah, well, Charlie would. *g* So I'm just saying that the notation used to write that out does not in fact represent what Thomasina would have actually literally said accurately. It's not horrible, but it's not right either. And I'm obsessive, but feeling too lazy to dig out a means of making the notation correct for the purposes of posting one comment.]

Re: Advanced

[identity profile] charlieeppes.livejournal.com 2005-10-21 03:30 pm (UTC)(link)
(ooc: Oh he totally would. *agrees* And, hee! That's fine. I'm delighted that you're doing the excercise at all. Seeing students replying makes me all beam-y and things.)

Re: Advanced

[identity profile] miss-thomasina.livejournal.com 2005-10-21 03:34 pm (UTC)(link)
[OOC: Hey, it's fun. And it's a delight and a pleasure to make you all beam-y and things. *grins and skritches the JakeCharlie-mun*]

Re: Advanced

[identity profile] miss-thomasina.livejournal.com 2005-10-21 04:42 pm (UTC)(link)
[OOC: *g* Now get back in character, you. We wanna play with Charlie.]
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