Can You Solve This Hilarious Limit Problem Involving Sine and Infinity?

[Galileo]

Not so much a joke as a brainteaser.

Three prisoners, strangers to each other, were suspects of a murder case. One day they came to hear that a sentence has been drawn. Two of them have been found guilty and will be executed, but they don't know which of the two . One guy, a statistician, figures his chances for survival are 1/3, so he goes to the bars of his cell and hails the guard: "Hey psst, do you know which of us has been sentenced?".
"Eh, yes.", says the guard, "But I'm not allowed to tell you.".
"Tell you what", says the guy, "I already know that 2 of us will executed, that means at least one of the other guys will be. I don't know them or anything, surely you can point to one which is guilty?". The guard sees no harm in that and points one of the prisoners, "He is guilty".
"Thanks!", proclaims the statistician, "my chances have just increased to 1/2".

 

[Reshma]

OK, here is another bad math joke:

What do you get when you cross a Pig and a Rat?

Answer: \mbox{Pig Rat}\sin \theta \hat n

 

[Joffe]

Thats an interesting puzzle Galileo, had me confused for a moment.

 

[Galileo]

A chemist, a physicist, and a mathematician are stranded on an island when a can of food rolls ashore. The chemist and the physicist comes up with many ingenious ways to open the can. Then suddenly the mathematician gets a bright idea: "Assume we have a can opener ..."

Sad, but true:
The Evolution of Math Teaching

1960s: A peasant sells a bag of potatoes for $10. His costs amount to 4/5 of his selling price. What is his profit?
1970s: A farmer sells a bag of potatoes for $10. His costs amount to 4/5 of his selling price, that is, $8. What is his profit?
1970s (new math): A farmer exchanges a set P of potatoes with set M of money. The cardinality of the set M is equal to 10, and each element of M is worth $1. Draw ten big dots representing the elements of M. The set C of production costs is composed of two big dots less than the set M. Represent C as a subset of M and give the answer to the question: What is the cardinality of the set of profits?
1980s: A farmer sells a bag of potatoes for $10. His production costs are $8, and his profit is $2. Underline the word "potatoes" and discuss with your classmates.
1990s: A farmer sells a bag of potatoes for $10. His or her production costs are 0.80 of his or her revenue. On your calculator, graph revenue vs. costs. Run the POTATO program to determine the profit. Discuss the result with students in your group. Write a brief essay that analyzes this example in the real world of economics.

Math problems? Call 1-800-[(10x)(13i)2]-[sin(xy)/2.362x].

Let the lameness commence!

Q: What's yellow, linear, normed and complete?
A: A Bananach space.

Q: What's yellow and equivalent to the Axiom of Choice.
A: Zorn's Lemon.

 

[Palindrom]

You people are sad...

Allow me to join you.


A mathematician, a physicist and a chemist are watching an empty house.
About ten minutes to their watch, they see two people go inside the house. All three of them write it down, and continue watching, when at their surprise, ten more minutes later, three people are seen leaving the house.
The biologist then says, "Well, there was probably someone inside and we didn't know about it".
The physicist replies, "No, no, it is a common mistake of measurement".
The mathematician looks at them both and states, "If one man were to enter the house now, it would be empty!".

 

[NateTG]

"Thanks!", proclaims the statistician, "my chances have just increased to 1/2".

Must be a Baysian.

 

[Physics Monkey]

At a party:

What do you do?
I'm interested in topology.
Oh, so you study maps?
Only continuous ones.

 

[LeonhardEuler]

Not so much a joke as a brainteaser.
Three prisoners, strangers to each other, were suspects of a murder case. One day they came to hear that a sentence has been drawn. Two of them have been found guilty and will be executed, but they don't know which of the two . One guy, a statistician, figures his chances for survival are 1/3, so he goes to the bars of his cell and hails the guard: "Hey psst, do you know which of us has been sentenced?".
"Eh, yes.", says the guard, "But I'm not allowed to tell you.".
"Tell you what", says the guy, "I already know that 2 of us will executed, that means at least one of the other guys will be. I don't know them or anything, surely you can point to one which is guilty?". The guard sees no harm in that and points one of the prisoners, "He is guilty".
"Thanks!", proclaims the statistician, "my chances have just increased to 1/2".

Alright, this is killing me! Can someone please explain it!

 

[ranger]

Sad, but true:
The Evolution of Math Teaching
1960s: A peasant sells a bag of potatoes for $10. His costs amount to 4/5 of his selling price. What is his profit?
1970s: A farmer sells a bag of potatoes for $10. His costs amount to 4/5 of his selling price, that is, $8. What is his profit?
1970s (new math): A farmer exchanges a set P of potatoes with set M of money. The cardinality of the set M is equal to 10, and each element of M is worth $1. Draw ten big dots representing the elements of M. The set C of production costs is composed of two big dots less than the set M. Represent C as a subset of M and give the answer to the question: What is the cardinality of the set of profits?
1980s: A farmer sells a bag of potatoes for $10. His production costs are $8, and his profit is $2. Underline the word "potatoes" and discuss with your classmates.
1990s: A farmer sells a bag of potatoes for $10. His or her production costs are 0.80 of his or her revenue. On your calculator, graph revenue vs. costs. Run the POTATO program to determine the profit. Discuss the result with students in your group. Write a brief essay that analyzes this example in the real world of economics.

I got a kick from that one

 

[jim mcnamara]

Back to pathetic:

Pi r squared.
No.
Pi r circles.

 

[uart]

Originally Posted by Galileo
Not so much a joke as a brainteaser.
Three prisoners, strangers to each other, were suspects of a murder case. One day they came to hear that a sentence has been drawn. Two of them have been found guilty and will be executed, but they don't know which of the two . One guy, a statistician, figures his chances for survival are 1/3, so he goes to the bars of his cell and hails the guard: "Hey psst, do you know which of us has been sentenced?".
"Eh, yes.", says the guard, "But I'm not allowed to tell you.".
"Tell you what", says the guy, "I already know that 2 of us will executed, that means at least one of the other guys will be. I don't know them or anything, surely you can point to one which is guilty?". The guard sees no harm in that and points one of the prisoners, "He is guilty".
"Thanks!", proclaims the statistician, "my chances have just increased to 1/2".

Alright, this is killing me! Can someone please explain it!

His chances have not changed as no new information (that would change the statics) was really added by the guards revelation.

One thing I do find weird about this problem is how two people whom have never meet can both be found guilty of the same murder. That's some pretty whacky justice system.

 

[GregA]

I don't really have much knowledge of stats and so I apologise if this seems like a stupid reply but I just have to chip in...

the three prisoners each have a 1/3 chance of survival...the guard however has just informed one prisoner that a different prisoner's chance of survival just dropped from 1/3 to 0/3...already the system has been changed no?
Also from the perspective of the statistician, before he found out who was doomed, the dice was weighted equally for all of them but now he can look at one prisoner and be absolubtely sure that his presence can have no effect on the outcome. (if we call the three prisoners A,B and C.., from C's perspective before speaking to the guard there are three people in the game. 'A' might die, but then again there is a chance that his luck is in and it will be B and C that die...knowing that 'A' is dead though, means there are only two people left in the game) thus his chances should be 1/2 no? (unless the guard is lying)
As I said earlier...my apologies If I am talking garbage

edit: had this discussion with a wiser person than myself and now know why I am wrong :)

 

[Denryoku]

Alright, this is killing me! Can someone please explain it!

Hi, this is my first post

I'm not really sure about this, but I agree with uart that no new significant information was given by the guard. I think the problem is in the way the prisoner simply eliminated the guy pointed by the guard from his reasoning.

Since we have no information about who commited the crime (or how the justice system works), we assume each one to have an equal chance of survival. At the beginning its clear that any given prisoner has a 1/3 chance of being declared innocent.

Later, one prisoner (say, prisoner A) asks the guard to point one of the other guys who is guilty. So he points one of the two suspects that will executed (lets say, prisoner B). Now A can figure his chances of survival using Bayes' theorem as follows:

P(A is innocent | B was pointed) = P(B was pointed | A is innocent) * P(A is innocent) / [ P(B was pointed | A is innocent) * P(A is innocent) + P(B was pointed | A is guilty) * P(A is guilty) ]

-The probability of B being pointed by the guard given that A is innocent is 1/2 (if A is innocent then the other two are guilty, but the guard had to point only one of them)
-The chances of A being innocent are still 1/3
-The probability of B being pointed by the guard given that A is guilty is, again 1/2 (since A is guilty, only one of the other two prisoners is guilty and thus was signaled by the guard; but we have no information to determine which one)
-The probability of A being guilty is 1 - 1/3 = 2/3

So the chances of A being innocent given that B was signaled by the guard are: (1/2 * 1/3) / (1/2 * 1/3 + 1/2 * 2/3) = 1/3 (not 1/2)


Well, back to the main topic... taken from http://www.xs4all.nl/~jcdverha/scijokes/1_6.html" :

A bunch of Polish scientists decided to flee their repressive
government by hijacking an airliner and forcing the pilot to fly them
to a western country. They drove to the airport, forced their way on
board a large passenger jet, and found there was no pilot on board.
Terrified, they listened as the sirens got louder. Finally, one of
the scientists suggested that since he was an experimentalist, he
would try to fly the aircraft.

He sat down at the controls and tried to figure them out. The sirens
got louder and louder. Armed men surrounded the jet. The would be
pilot's friends cried out, "Please, please take off now! Hurry!"

The experimentalist calmly replied, "Have patience. I'm just a simple
pole in a complex plane."

 

[murshid_islam]

don't know whether this one's posted already:

a mathematician is one who cannot tell a teapot from a doughnut.

 

[fourier jr]

don't know whether this one's posted already:
a mathematician is one who cannot tell a teapot from a doughnut.

i think you mean coffee cup and a doughnut, since a teapot has 2 handles while a doughnut has only 1

 

[murshid_islam]

i think you mean coffee cup and a doughnut, since a teapot has 2 handles while a doughnut has only 1

well, the teapots i have seen have only one handle. anyway, the point is that both a doughnut and a teapot with one handle (or a coffee cup) has one hole in it. in the doughnut, the hole is in the middle, whereas in the coffee cup, it is in the handle.

 

[benorin]

don't know whether this one's posted already:
a mathematician is one who cannot tell a teapot from a doughnut.

That sounds more like a topologist.

 

[NateTG]

well, the teapots i have seen have only one handle. anyway, the point is that both a doughnut and a teapot with one handle (or a coffee cup) has one hole in it. in the doughnut, the hole is in the middle, whereas in the coffee cup, it is in the handle.

I think we have a new candidate -- "A topologist is someone who thinks that most teapots have two handles."

Most teapots I am familiar with have two holes (or handles) in them. One that your fingers go through, and the other that tea goes through.

 

[hypermorphism]

The spout for the tea is not equivalent to a handle (a torus with a disc removed). If anything, the teapot (without the lid) would be equivalent to a (circular) cylinder with a handle attached. The equivalence of the coffee cup and the donut has less ambiguity. :)

 

[shmoe]

The spout for the tea is not equivalent to a handle (a torus with a disc removed). If anything, the teapot (without the lid) would be equivalent to a (circular) cylinder with a handle attached. The equivalence of the coffee cup and the donut has less ambiguity. :)

A teapot is a two handled coffee cup. If your cylinder+handle hopes to be a teapot then the cylinder part has thickness, i.e. a 3 dimensional volume (like a coffee cup with a hole in the bottom). This can be deformed into a two handled coffee cup for safety purposes or into a two holed donut for delicousness.

Think of the classification theorem of compact connected orientable 2-manifolds without boundary (did I get everything?). The surface of the teapot is one of these, hence it's either a sphere or torus with some number of handles.

 

[podboy6]

Worst math joke ever:

"Okay, when you rotate a conic section, you slap on -iod to the end of its name, i.e, paraboloid, hyperboloid, ellipsiod, ect...

Okay, what do you get when you rotate a human?

A humaniod."

 

[uart]

Hi, this is my first post
Since we have no information about who commited the crime (or how the justice system works), we assume each one to have an equal chance of survival. At the beginning its clear that any given prisoner has a 1/3 chance of being declared innocent.
Later, one prisoner (say, prisoner A) asks the guard to point one of the other guys who is guilty. So he points one of the two suspects that will executed (lets say, prisoner B). Now A can figure his chances of survival using Bayes' theorem as follows:
P(A is innocent | B was pointed) = P(B was pointed | A is innocent) * P(A is innocent) / [ P(B was pointed | A is innocent) * P(A is innocent) + P(B was pointed | A is guilty) * P(A is guilty) ]
-The probability of B being pointed by the guard given that A is innocent is 1/2 (if A is innocent then the other two are guilty, but the guard had to point only one of them)
-The chances of A being innocent are still 1/3
-The probability of B being pointed by the guard given that A is guilty is, again 1/2 (since A is guilty, only one of the other two prisoners is guilty and thus was signaled by the guard; but we have no information to determine which one)
-The probability of A being guilty is 1 - 1/3 = 2/3
So the chances of A being innocent given that B was signaled by the guard are: (1/2 * 1/3) / (1/2 * 1/3 + 1/2 * 2/3) = 1/3 (not 1/2)
:

Ouch Denryoko, I really think it can be put a lot more simply than that :). You're right to use Bayes thm with this type of problem however I'd prefer to tackle it as follows,

Define the events as follows,
Event A : Person asking guard is innocent.
Event B : Person picked out by guard is guilty.

The reason why this one is so simple is that P(B)=1 because it is given as data!

Now since P(B)=1, it is trivial that P(A and B) = P(A) hence Bayes theorem gives,

P(A | B) = P(A and B) / P(B) = P(A)

That is, the probability of event A given that event B has occurred is identical with the original probability of event A, so it remains at 1/3. This is really a trivial application of Bayes in this case.

---------------------------------

It's interesting to note that if you change the problem so that the guard does not have to pick guilty but instead selects one of the other two at random to reveal that persons fate (say by withdrawing a name from a hat or whatever) then you do end up with a non-trivial application of Bayes thm. In this case then the probability of the original guy's innocence does indeed rise from 1/3 up to 1/2 if the guard reveals one of the other two to be guilty. Using the same event definitions as above you now get the following,

P(A and B) = P(A), because if the original person is innocent then both the other two are guilty so the name withdrawn from the hat (or whatever) must be guilty.

This time however P(B) is not equal to unity but is instead P(B)=2/3.

So Bayes thm results in,

P(A | B) = P(A and B) / P(B) = 1/3 divide 2/3 = 1/2

I hope that helps anyone who was still unsure about that one.

 

[biggins]

another joke

alcohol and calculus don't mix, don't drink and derive.

 

[Lisa!]

A real mathematician is someone who writes 'A', then read it 'B', but actually he means 'c'.

 

[benorin]

I'm supposed to prove the freshman’s dream identity,

\left( a + b\right) ^p \equiv a^p + b^p \left( \mbox{mod }p\right)

for p prime.

Can't I just use the binomial theorem? j/k

 

[benorin]

How they prove that all odd integers higher than 2 are prime?

How they prove that all odd integers higher than 2 are prime?

Mathematician: 3 is a prime, 5 is a prime, 7 is a prime, and by induction - every odd integer higher than 2 is a prime.

Professor: 3 is prime, 5 is prime, 7 is prime, and the rest are left as an exercise for the student.

Physicist: 3 is a prime, 5 is a prime, 7 is a prime, 9 is an experimental error, 11 is a prime,...

Engineer: 3 is a prime, 5 is a prime, 7 is a prime, 9 is a prime, 11 is a prime,...

Programmer: 3 is a prime, 5 is a prime, 7 is a prime, 7 is a prime, 7 is a prime,...

Salesperson: 3 is a prime, 5 is a prime, 7 is a prime, 9 -- we'll do for you the best we can,...

Computer Software Salesperson: 3 is prime, 5 is prime, 7 is prime, 9 will be prime in the next release,...

Biologist: 3 is a prime, 5 is a prime, 7 is a prime, 9 -- results have not arrived yet,...

Advertiser: 3 is a prime, 5 is a prime, 7 is a prime, 11 is a prime,...

Lawyer: 3 is a prime, 5 is a prime, 7 is a prime, 9 -- there is not enough evidence to prove that it is not a prime,...

Accountant: 3 is prime, 5 is prime, 7 is prime, 9 is prime, deducing 10% tax and 5% other obligations.

Statistician: Let's try several randomly chosen numbers: 17 is a prime, 23 is a prime, 11 is a prime...

Computational linguist: 3 is an odd prime, 5 is an odd prime, 7 is an odd prime, 9 is a very odd prime,...

Psychologist: 3 is a prime, 5 is a prime, 7 is a prime, 9 is a prime but tries to suppress it,...

I coppied this from here.

 

[Galileo]

A real mathematician is someone who writes 'A', then read it 'B', but actually he means 'c'.

Sounds like my professor. He writes A, says B, means C, while the answer is D.

 

[hypermorphism]

...
Think of the classification theorem of compact connected orientable 2-manifolds without boundary (did I get everything?). The surface of the teapot is one of these,...

Ah, then you're including the fact that the teapot contains a non-zero 3-dimensional volume, or the surface of a 3-dimensional manifold analogous to a teapot. I was thinking of a 2-dimensional manifold analogous to a teapot, in that the handle was attached to a sphere with two discs removed. In that case, my teapot does have a boundary, but yours doesn't.

 

[uart]

prove the identity,
\left( a + b\right) ^p \equiv a^p + b^p \left( \mbox{mod }p\right)
for p prime.
Can't I just use the binomial theorem? j/k

What's wrong with using the binomal theorem there ?

 

[Lisa!]

https://www.physicsforums.com/showpost.php?p=805754&postcount=268"

Sounds like my professor. He writes A, says B, means C, while the answer is D.

But he must be a bad mathematician since he doesn't get the answer!