For the discussion of math. Duh.

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btilly
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### Re: Amusing answers to tests

Torn Apart By Dingos wrote:
btilly wrote:The professor said that I was absolutely right, and in all of the years that he'd been giving the course I was the only person to figure that out. Then he told me where I could find the article giving the difficult counter-example.

What is the counter-example? Also, what text did you use?

The book was Foundations of Mathematical Analysis. I never looked up the counter-example, and if I had I'd have forgotten about it by now (this happened 16 years ago). If you enjoy such things, I'd suggest reading Counter-examples in Analysis.

As for the specific question I posed (which may or may not be the one I was asked), this book points to an answer. (I suspect I was asked a different question given that it is well-known that L1 contains functions that are not in L2. Perhaps a product of Riemann-Stieltjes integrable functions that is not Riemann-Stieltjes integrable?)
Some of us exist to find out what can and can't be done.

Others exist to hold the beer.

jestingrabbit
Factoids are just Datas that haven't grown up yet
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### Re: Amusing answers to tests

Torn Apart By Dingos wrote:What is the counter-example? Also, what text did you use?

A simple counter example (that doesn't need Lebesgue measurability) is the functions f(x)=g(x) = x-1/2 for 0<x<1 and 0 otherwise. The antiderivative tells you that the integral is finite and when you form the product you get 1/x for 0<x<1 and 0 otherwise, which doesn't have a (finite) integral.

Not that difficult a counter example, must have been a different question.
ameretrifle wrote:Magic space feudalism is therefore a viable idea.

DemonHybrid
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### Re: Amusing answers to tests

scowdich wrote:There's a mythical final exam given by a philosophy professor: he places a chair at the front of the room, passes out blue books, and says "Prove this chair doesn't exist."

Legendarily, the only A was garnered by a student who wrote "What chair?"

I don't get it. Isn't that debunked by the "Just because you believe something, doesn't make it true" saying?

Just because I can say that the chair isn't there doesn't mean it isnt.
"If we value the pursuit of knowledge, we must be free to follow wherever that search may lead us. The free mind is not a barking dog, to be tethered on a ten-foot chain."

scowdich
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### Re: Amusing answers to tests

And just because you say the chair is there doesn't mean it actually is. And here we come to the point of the exercise...

gmalivuk
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### Re: Amusing answers to tests

jestingrabbit wrote:
Torn Apart By Dingos wrote:What is the counter-example? Also, what text did you use?

A simple counter example (that doesn't need Lebesgue measurability) is the functions f(x)=g(x) = x-1/2 for 0<x<1 and 0 otherwise. The antiderivative tells you that the integral is finite and when you form the product you get 1/x for 0<x<1 and 0 otherwise, which doesn't have a (finite) integral.

Not that difficult a counter example, must have been a different question.

1/x is most certainly Lebesgue integrable. Your not difficult example fails pretty hard at actually being a counterexample, so I suspect it wasn't a different question.
Unless stated otherwise, I do not care whether a statement, by itself, constitutes a persuasive political argument. I care whether it's true.
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antonfire
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### Re: Amusing answers to tests

Not according to MathWorld. Usually, a function with an infinite integral isn't considered integrable. (I'm not saying that this is "the right way", but it's apparently a common enough convention that it's the one on MathWorld.)

I'm assuming that you mean that 1/x is measurable. The question can't have been about that, because the product of two measurable functions is measurable (and I'm sure any analysis text would mention this).
Jerry Bona wrote:The Axiom of Choice is obviously true; the Well Ordering Principle is obviously false; and who can tell about Zorn's Lemma?

jestingrabbit
Factoids are just Datas that haven't grown up yet
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### Re: Amusing answers to tests

@gmalivuk: what antonfire said. Otherwise, why have the two words integrable and measurable?

Though I did realise that 1/x isn't bounded on every finite width interval so it isn't properly Riemann integrable. You can get around that by "breaking it up" into a countable collection of intervals, and translating them to places that are a fixed distance from one another. But again, not really all that difficult.
ameretrifle wrote:Magic space feudalism is therefore a viable idea.

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### Re: Amusing answers to tests

DemonHybrid wrote:
scowdich wrote:There's a mythical final exam given by a philosophy professor: he places a chair at the front of the room, passes out blue books, and says "Prove this chair doesn't exist."

Legendarily, the only A was garnered by a student who wrote "What chair?"

I don't get it. Isn't that debunked by the "Just because you believe something, doesn't make it true" saying?

Just because I can say that the chair isn't there doesn't mean it isnt.

I think the point is by trying to prove that it doesn't exist the students are validating its existence.
Guys guys guys! I found Russel's teapot! . . . nevermind, it was just Jesus flying to Mars again.

Iori_Yagami
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### Re: Amusing answers to tests

Please tell me whether I have forgotten all school (and 1st year Uni)physics or not -
the guy who drew an elephant in OP solved almost everything, but forgot to equate two energies? So m * g * h = k * x2 And the object would never stop, because there is no friction? Or am I missing something?
They cannot defend themselves; they cannot run away. INSANITY is their only way of escape.

scowdich
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### Re: Amusing answers to tests

Well, the object would stop for an infinitesimal amount of time when the spring is at maximum compression...I believe the problem is asking what that maximum compression would be.

hyperion
"I'll show ye...."
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### Re: Amusing answers to tests

A friend's answer for the chemistry exam the week before last. The question was something along the lines of
You are a hydrogen molecule in a balloon filled with equal moles of hydrogen and oxygen molecules at 2 atm pressure. A student ignites the balloon with a match. Describe:
1) What you see initially
2) What you see during combustion
3) Your life as a water molecule

I wrote an equally strange essay, and even managed to play the cheesecake game, but my scanner's broken so you can't see it.
Peshmerga wrote:A blow job would probably get you a LOT of cheeseburgers.
But I digress.

aguacate
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### Re: Amusing answers to tests

HYPERiON wrote:A friend's answer for the chemistry exam the week before last. The question was something along the lines of
You are a hydrogen molecule in a balloon filled with equal moles of hydrogen and oxygen molecules at 2 atm pressure. A student ignites the balloon with a match. Describe:
1) What you see initially
2) What you see during combustion
3) Your life as a water molecule

10/20, that blows.

hyperion
"I'll show ye...."
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### Re: Amusing answers to tests

aguacate wrote:10/20, that blows.

The average was 4/20 and the top was something like 15, so it's pretty good.
Peshmerga wrote:A blow job would probably get you a LOT of cheeseburgers.
But I digress.

Zohar
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### Re: Amusing answers to tests

HYPERiON wrote:

Very nice. Reminds me of Flatland.
Mighty Jalapeno: "See, Zohar agrees, and he's nice to people."
SecondTalon: "Still better looking than Jesus."

Not how I say my name

oxoiron
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### Re: Amusing answers to tests

HYPERiON wrote:
aguacate wrote:10/20, that blows.

The average was 4/20 and the top was something like 15, so it's pretty good.

It still blows. I've graded a LOT of chemistry papers, and that is without a doubt the most entertaining one I've ever seen. The grader had a serious stick up his butt.
"Whenever you find yourself on the side of the majority, it is time to reform (or pause and reflect)."-- Mark Twain
"There is not more dedicated criminal than a group of children."--addams

Not an Evil Robot
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### Re: Amusing answers to tests

Today was my Discrete Structures Final.
I did it pretty fast but there was one extra credit question I had no idea on.
So I drew a big cookie and wrote

thats the best I've got =(

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### Re: Amusing answers to tests

I've just finished my insane topology homework for the semester. This question in particular drove me crazy. Not a test, but there aren't any for the class, so I think this counts. Incidentally, if anyone knows how to do this problem, I'd be interested.

Geekthras
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### Re: Amusing answers to tests

I know someone who was writing a paper on Zen Buddhism. They carefully controlled their word and paper length so that the last sheet contained the following:
"thus."

It was win. I once was unable to prove something in Geometry, so at a step that I couldn't do, I just ignored the fact that it didn't follow (I think I was using Angle-Side-Side) and put in the explanation column two up arrows, two down arrows, <- -> <- ->, the letters B and A in circles, and the word START.
Wait. With a SPOON?!

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### Re: Amusing answers to tests

not math, but I answer every case study question I don't know in my anatomy and physiology class with "It could be lupus..."
Guys guys guys! I found Russel's teapot! . . . nevermind, it was just Jesus flying to Mars again.

Sly Si
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### Re: Amusing answers to tests

One of my friends (who may actually end up reading this at some point) and I had a very difficult math class last spring. As most of the students were grad students furiously preparing for quals, we knew the prof was going to go easy on us. There were only two problem sets and no exams, and we figured everyone would get A's (we were right). That was lucky, because the material was difficult and no one understood what was going on in lecture.

Anyway, on the last problem of the second problem set, neither of us had any idea what to do. And it was about 3 AM, so we were ready to give up. My friend, not wanting to turn in a blank sheet, drew Trogdor the Burninator on a piece of notebook paper, complete with Strong Bad's instructions on how to draw him. He labeled it "#6", stapled it to the rest of his answers, and turned it in.

He got partial credit--1/10--and a complement from the TA. Hopefully I can get him to scan it if he still has it and post it somewhere.

phantom
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### Re: Amusing answers to tests

not quite a test answer, but it kind of goes along. I found this on http://www.kent.k12.wa.us/staff/DavidWr ... jokes.html

The Calculus Final
Gelsamel wrote:
Vaniver wrote:I'm claiming that the programming itself is the free will.

10 PRINT "Hello World"
20 GOTO 10
Yeah, the computer is using it's free will to display "Hello World" over and over again.

Zohar
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### Re: Amusing answers to tests

^ That was in Veronica Mars.
Mighty Jalapeno: "See, Zohar agrees, and he's nice to people."
SecondTalon: "Still better looking than Jesus."

Not how I say my name

Azrael001
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### Re: Amusing answers to tests

That is a good story, even though I have heard it before.

When I know that I don't know the answer on a test I tend to do silly things. In most math type subjects I will let x be equal to the correct answer, and simply answer x, after of course adding the above constraint. I have also written a function to call the answer with the answer sheet included as an outside file.
23111

3.14159265...
Irrational (?)
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### Re: Amusing answers to tests

Wholy crap, thats a nice story.
"The best times in life are the ones when you can genuinely add a "Bwa" to your "ha""- Chris Hastings

Kizyr
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### Re: Amusing answers to tests

Zohar wrote:^ That was in Veronica Mars.

I actually heard that story years ago (about 6-7 years ago), so it's pretty old and relatively well-known.

It's still a really good one, though. In the version I usually told, I said it was my cousin at Berkeley who was the main character. KF
~Kizyr

Macbi
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### Re: Amusing answers to tests

I can't find it now, but I saw a video of this on YouTube or some such site.
Indigo is a lie.
Which idiot decided that websites can't go within 4cm of the edge of the screen?
There should be a null word, for the question "Is anybody there?" and to see if microphones are on.

korhonenpt
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### Re: Amusing answers to tests

Out of boredom I did this... please tell me if my answers are correct?

Well at first we'll have to find the velocity at which the object touches the spring. Let's call its initial position a and the maximum extended position of the spring (just as it touches it) b.

It has gravitational potential energy at A, and kinetic and b. therefore;

Ega=Ekb

mgha=.5mvb2

vb=sqrt(2gha)=sqrt(2(9.81m/s2)(5m))=9.9045m/s.

Now that we have the velocity at which the object impacts the spring, we can calculate how much the object will compress it. (x) We will call the compressed position c.

Ekb=Eec

1/2mva2=1/2kxc2

xc=sqrt((mva2)/k)

xc=sqrt((3kg)(9.9m/s)2)/100N/M))=1.71m

So the answer to the first question is that x, or the distance the spring will be compressed, is therefore 1.7 m.

Before doing the equation, since there is no friction, I'm pretty sure that means that it will go back up the ramp 5m? I'll prove it just to make sure... Let's call however high it gets d.

Eec=Egd

1/2kc2=mghd

hd=(kxc2)/2mg

hd=(100n/M(1.71m)2)/(2)(3kg)(9.81m/s)
hd=4.967m
hd=5.0m

The only reason it was a bit off was because sqrt(2(9.81m/s)(5)) was converted and rounded to decimal form.
yay, physics?

skeptical scientist
closed-minded spiritualist
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### Re: Amusing answers to tests

korhonenpt wrote:

Out of boredom I did this... please tell me if my answers are correct?

More or less, but you are spending way too much effort:

Since there is no friction, the only energies in the problem are gravitational potential (mgh), spring potential (1/2kx2), and kinetic (1/2mv2). So conservation of energy tells you that when the mass is at rest (i.e. when the spring is most compressed or the block is at the top of the slope), all energy will be in one or the other of the potential forms. So it will oscillate between its starting position (all energy in gravitational potential, so height is always same as height at start) and compressing the spring by sqrt[2(3kg)g(5 m)/(100 N/m)]~1.7 m.
I'm looking forward to the day when the SNES emulator on my computer works by emulating the elementary particles in an actual, physical box with Nintendo stamped on the side.

"With math, all things are possible." —Rebecca Watson

Macbi
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### Re: Amusing answers to tests

But you're both wrong- There is an elephant in the way.
Indigo is a lie.
Which idiot decided that websites can't go within 4cm of the edge of the screen?
There should be a null word, for the question "Is anybody there?" and to see if microphones are on.

Iori_Yagami
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### Re: Amusing answers to tests

So I was right (only lost that 1/2 on my way).
They cannot defend themselves; they cannot run away. INSANITY is their only way of escape.

sward
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### Re: Amusing answers to tests

Again not math.

I'va had half a year of latin and we all dreaded that class. There were three active students, one who considered latin fascinating, and two boys who considered our young female teatcher hot.

Anyways a boy from my class was called to the blackboard, we often were to give an analyzation of a given sentence, so he stood there staring at the blackboard, our teatcher wanting to move on asked "now what do you wanna do with that?", the he took the eraser and cleared the blackboard and announced "Done!"...

In retrospective I'm kinda sorry for my teatcher we were her first class, and we all hated her subject...

roundedge
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### Re: Amusing answers to tests

In one of my math finals this semester, I was trying to factor out an (x^2-y^2) from an equation (I can't remember the specific equation). Anyways, for some reason I couldn't do it. So after covering my page in figuring and rough work, I finally gave up, drew a picture of cthullu wrapping his tentacles around the equation and wrote "Cthullu sucks the (x^2 -y^2) straight out of the equation! A truly otherworldly feat! Tremble at the power of Cthullu! QED"

Whenever I do math tests, I frequently write down my thought processes, even if those thought processes have little to do with the math. I was trying to solve an ODE this semester using variation of parameters, because undetermined coefficients method had proved unsuccessful, but I couldn't remember the exact form of the huge equation that goes along with it, so I wrote "let's see if I can remember this sucka." Wrote down what I thought was the equation, realized I'd blanked on how to do the wronskian, wrote "5 minutes till the exam is over, and then it's christmas, fuck the wronskian" Turned back a couple pages to a blank page that said "for rough work, will not be marked" and drew a picture of a ghost to surprise my TA after he had cruised through marking the true or false sections.

Boatz!
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### Re: Amusing answers to tests

An old Religious Studies one I heard.

Q: What's a Hindu?
A: It lays eggs
Remember, eating mushrooms is illegal on other planets. Especially Jupiter. I dunno what those guys eat. o_O

phantom
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### Re: Amusing answers to tests

More of an amusing question than answer, but this happened today, so here goes. Our calculus teacher doesn't like to give us tests on mondays if at all possible, but the scheduling made it so she had to. To make up for it, she gave us two bonuses. One was, I think, take the derivative of arcsin(arctan(sqrt(x))). The other was: "What christmas present do I want to get for my daughter this year?" She'd been talking about how she can't find a Hannah Montana guitar for her daughter for the last few weeks, making it five free points for all of us
Gelsamel wrote:
Vaniver wrote:I'm claiming that the programming itself is the free will.

10 PRINT "Hello World"
20 GOTO 10
Yeah, the computer is using it's free will to display "Hello World" over and over again.

Geekthras
3) What if it's delicious?
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### Re: Amusing answers to tests

About 3/4 of the way, through, conversation breaks off and goes in a completely different direction.
Wait. With a SPOON?!

Azrael001
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### Re: Amusing answers to tests

I was just reading through Java Pirates and came across this comic... it fits even though it's fiction.

This should work now.
Last edited by Azrael001 on Thu Dec 20, 2007 4:45 am UTC, edited 1 time in total.
23111

bobtpawn
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### Re: Amusing answers to tests

A friend and I were taking an abstract algebra class together and there was one homework problem we just couldn't answer. So, my friend answers, "This is the sixth edition of this book, so the probability that the problem is in error is well within acceptable bounds. Since they would not ask us to prove something false, the statement must be true."

pkuky
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### Re: Amusing answers to tests

theree was a question on a phisics test that went "draw a graph of the place and velocity of the ball as dependent on time", so someone drew a zero graph and wrote "the observer is sitting on the ball".
It rains on the enemy too!

Govalant
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### Re: Amusing answers to tests

Azrael001 wrote:I was just reading through Java Pirates and came across this comic... it fits even though it's fiction.

Can't see it :/.
Now these points of data make a beautiful line.

How's things?
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spectacu-awesome
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### Re: Amusing answers to tests

In chem, (electrolysis) no one in the class could figure out what was the source of the loss of efficiency in a copper electro-refining cell (it had an actual efficiency of 3%). So, tiny tiny goblins swam out of the anode to steal charges from the solution and bring them back to the anode. Goblins are the ultimate answer for anything chemical that can't be explained.
Graphing rational functions is a pain in the asymptote
We're number -[e^(pi*i)]