## 1. MATHEMATICS

#### Subsections

- 1. mathematics - general
- 1.1 proofs
- 1.2 statistics and statisticians
- 1.3 mathematicians
- 1.4 mathematics poetry
- 1.5 mathematics quotes
- 1.6 mathematic puns
- 1.7 mathematical terms
- 1.8 mathematical exams
- 1.9 learning mathematics
- 1.10 mathematical tests to take
- 1.11 mathematical equations
- 1.12 topology
- 1.13 numbers
- 1.14 set theory
- 1.15 functions

### 1.8 MATHEMATIC EXAMS

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    From:         "Simon" <spook@earthcorp.com>

#### Gauteng Province (Johannesburg) - New Maths Exam

Please all read instructions carefully:

    Please write all answers between the lines.
    No part of the answer book may be rolled and smoked.
    No children of students are allowed to participate.
    Please leave firearm in possession of parole offices.
    Bribes will be accepted at a minimum of R100.
    If this exam does not match the one you have bought in advance, please
    notify the examiner.

##### QUESTION 1

Philemon has an AK47 with 2 magazines taped together, each holding 30 rounds. If he misses 8 out of 10 shots, how many drive-by taxi shootings can he attend before having to reload?

##### QUESTION 2

Phineas has a 12 seater minibus, but to avoid discomfort he never carries more than 23 people. Assuming each passenger weighs 85 kg and piles 35 kg of luggage on the roof, he drives 140 km/h and that his brakes are 25% efficient, what would his stopping distance be?
a) 300m b) 600m c) 10m as there is another passenger to pick up.

##### QUESTION 3

Jacob is employed as a garden boy for one day a week for 5 households. Assuming that he can make a lawn mower last 3 months, how many lawn mowers will the household have to buy in a period of 2 years.

##### QUESTION 4

In standard 6, Jackson has made 4 girls pregnant and another 6 from other classes. How many girls will he have got pregnant before he leaves school if he matriculates on his 20th birthday?

##### QUESTION 5

Samuel and his friends, altogether 6 of them, can each drink 35 bottles per day of Castle Lager before falling over. How many SAB trucks do they need to hijack per year to remain permanently pissed?

mathematics
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    From: Satyre
                                MID-TERM MATH EXAM

                                  EBONICS VERSION

    Directions: Make sho yo be putting yo name on the upper rite hand
    comer. Don't be axin' no dumbass questions an keep yo shifty
    mothafuckin' eyes on yo own sorryass papers.

    Number 1 (25%)
    Elon and Tyrell bot want to meet fo lunch. Elon's home be 5 mile north
    of Tyrell. If Elon leave at 10:30 bookin bout 3 mile per hour while
    Tyrell, who have one coolass bike, ain't not departin' till I 1:00
    zoomin bout 20 mile per hour, what time be Elon axin' Tyrell for a
    bite of fiied chicken?

    Number 2 (25%)
    Yolanda, she be 11 year older than her daughter Carinda. Carinda have
    a bitch Carmel who haf her age. In how many years be Carmel haf as old
    as that uglyass ho Yolanda?

    Number 3 (40%)
    If Leroy axes Marvin fo 10 gram of 60% coke an Marvin ain't not got
    nothing but 8 gram of 80% and some ol 20% shit, how much of the cheap
    stuff be Marvin mixing up so Leroy can go off the hizzie?

    Number 4 (10%)
    Lenwood and Keshawn jus lifted one gross of basketballs offa Kmart. If
    studly Lenwood can dunk fo mo balls per minute than Keshawn, how long
    be these bros slammin and jammin fo they be needin suh mo balls to
    play wif?

    Extra Credit (5 points)
    Which number, A or B be bigger? Make sho you shows all yo work.

    A. The total number of hos Wilt Chamberlain and B.B. King be sleeping
    wif.

    B. The number of yard OJ done ran fo in his best season timeses the
    number a cuts he be putting in that nogood honkey bitch Nicole afta
    catchin her wif a guy what ain't got no goddam mothafuckin rights be
    ridin roun wif OJs car.

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                           Los Angeles High School Math Exam

    1. Johnny has an AK47 with a 40 round clip. If he misses 6 out of 10 shots
    and shoots 15 times each drive by, how many drive by shootings must he
    conduct before he shoots 50 people?
    2. Paul has 2 ounces of cocaine and he sells 10 grams to Jackson for $820,
    and 2 grams to Billy for $85 per gram. What is the street value of the
    balance of the cocaine if he doesn't cut it?
    3. Willie gets $200 for stealing a BMW, $50 for a Chevy and $100 for a 4x4.
    If he has stolen two BMWs and three 4x4s, how many Chevys will he have to
    steal to make $800?
    4. If the contents of an average can of spray paint covers 22 square feet
    and the average letter is eight square feet, how many letters can a
    teenager spray with eight cans of paint?
    5. Hector got six girls in his gang pregnant. There are 27 girls in the
    gang. What percentage of girls in the gang has Hector knocked up?
    6. Kathy gets $125 for sneaking an illegal alien across the border from
    Mexico. She sneaked three illegals over the border every night for six days
    but then one of them ripped her off for $500. How much money does she have
    left?
    7. Byron can trade $150 worth of food stamps for two tickets to a Lakers
    regular season game. If a play-off game costs 20 percent more, how many
    play-off tickets can he get for $500 in food stamps? From:

    From: jdmcmine@coop2.b11.ingr.com (Jeff)

    Answers to City of Los Angeles High School Math Proficiency Exam

    1. Johnny has an AK47 with a 40 round clip. If he misses 6 out of 10 shots
    and shoots 15 times each drive by, how many drive by shootings must he
    conduct before he shoots 50 people?

     Johnny hits 15*(4/10) people per drive by, which means that he
     will have to participate in 9 drive bys to shoot 50 people.
     However, he will have completed two drive-by shootings and be
     just starting the third when he has to reload. Since he only
     stole a single clip, he'll only have shot 16 people when the
     homeboys with the UZIs' make Swiss cheese out of him.

    2. Pony has 2 ounces of cocaine and he sells an 8 ball to Jackson for
    $320 and 2 grams to Billy for $85 per gram. What is the street value
    of the balance of the cocaine if he doesn't cut it?

     At 454 grams per pound, 2oz of the rock = 56.75 grams. An "8
     ball" is 8 grams, so pony has sold 10 grams total and has 46.75
     grams left. If he keeps selling 8-balls, he can sell 5 more (for
     a total of 5*$320=$1,600) and have 6.75 grams for his own nose.
     If he sells 2 gram packs, he can sell (46/2-23) packs at $85
     apiece = (23*$85)=$1,955. However, he could divide it into small
     parts, bake it up into crack and sell the rocks for an even
     larger profit. This problem is really more suited for the Gang
     Multi-Variable Economics Test.

    3. Ron is pimping for 3 girls. If the price is $65 for each trick,
    how many tricks will each have to turn so Ron can pay for his $800
    per day crack habit.

     800/$64=12 tricks plus a dance. Also, Ron should consider making
     a deal with Pony from Question #2.

    4. Susan wants to cut her 1/2 pound of heroin to make 20% more profit.
    How many ounces of cut will she need?

     If she sells the cut heroin at the same price per unit volume,
     she will need 20% more volume. 20% of 1/2 pound (=8oz) is 1.6oz.
     So, Susan will need 1.6oz of cut to add to the 8 oz of heroin to
     get 20% more volume. She will want a cut which looks similar to
     raw heroin and has approximately the same melting point. Plain
     sugar or laundry detergent are suggested. Laundry detergent has
     the added benefit of removing the possibility of customer
     complaints, but will sharply limit repeat business.

    5. Blade gets $200 for stealing a BMW, $50 for a Chevy, and $100 for
    a 4x4. If he has already stolen 2BMW's and 3 4x4's, how many Chevy's
    will he have to steal to make $800?

     Blade has made 2*$200 + 3*$100=$700 dollars from his theft so
     far. He needs $100 more, so he needs to steal $100/$50=2 more
     Chevy's. However, he will probably want to steal 4 Chevy's so he
     can take the extra two and make a really def low-rider.

    6. Little Willy is in prison for 6 years for murder. He got $25,000
    for the hit. If his common law wife is spending $250 per month, how
    much money will be left when he gets out of prison and how many
    years will he get for killing the bitch that spent his money?

     6 years*12 months/year*$250/month=$18,000. Little Willy will
     have $25,000 - $18,000 = $7,000 left when he gets out of prison.
     If Little Willy kills her in the USA, he should expect to get 6
     years. However, if he takes her down to Mexico and buries her
     scrawny, track-marked butt in the desert, he can get off scott
     free.

    7. If the average can of spray paint covers 22 square feet, and
    the average letter is 4 square feet, how many letters can a tagger
    spray with 3 cans of paint?

     3 cans of paint will cover 3*22=66 square feet. 66/4=16 letters
     with a little paint left over to spray in the eyes of the cop
     who's comin' after you. Or the tagger could do 15 letters and a
     bitchin' skull.

    8. Hector knocked up 6 girls in his gang. There are 27 girls in the
    gang. What percentage of the girls in the gang has Hector knocked up?

     6/27=22% of the girls. However, 2 of them are lying because
     they've been sleeping with Pedro, Hector's lieutenant. So, in
     actuality, Hector only knocked up 4/27 or 14.8%.

    9. Rosie's sole source of income is shoplifting. If she gets 10 cents on
    the dollar from her fence, how much merchandise must she shoplift each
    week to make $250.

     Solve X/10=250 for X, X=$2,500.

    10. Mike carjacked a Chevy Camaro for his date Saturday night with his
    young 14 year old girlfriend. He was arrested that night while making his
    girlfriend in the backseat. How much prison time is he looking for for the
    carjacking and for statutory rape, even though the girl looked legal?
    Assume no prior convictions in arriving at your answer.

     Mike is only 12 so he will serve no time and will be making
     his girlfriend in the lot in someone else's car next Saturday.

mathematics
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    From: "*G - P*" <G*P@G*P.Com>
                  SOCIO-MATH PROBLEMS FOR SAN FRANCISCO STUDENTS

    1). Zelda and Jane were given a rottweiler at their commitment ceremony. If
    their dog needs to be walked two miles a day and they walk at a rate of 1/2
    mile per hour, how much time will they spend discussing their relationship
    in public?

    2). Michael has two abusive stepfathers and an alcoholic mother. If his
    self-esteem is reduced by 20% per dysfunctional parent, but Michael feels
    3% better for every person he denigrates, how long will it take before he's
    ready to go home if 1 person walks by the cafe every 2 minutes?

    3). Sanjeev has 7 piercings. If the likelihood of getting cellulitis on a
    given day is 10% per piercing, what is the likelihood Sanjeev will need to
    renew his erythromycin prescription during the next week?

    4). Chad wants to take half a pound of heroin to Orinda and sell it at a
    20% profit. If it originally cost him $1,500 in food stamps, how much
    should Nicole write the check for?

    5). The City and County of San Francisco decide to destroy 50 rats
    infesting downtown. If 9,800 animal rights activists hold a candlelight
    vigil, how many people did each dead rat empower?

    6). A red sock, a yellow sock, a blue sock, and a white sock are tossed
    randomly in a drawer. What is the likelihood that the first two socks drawn
    will be socks of color?

    7). George weighs 245 pounds and drinks two triple lattes every morning. If
    each shot of espresso contains 490mg of caffeine, what is George's average
    caffeine density in mg/pound?

    8). There are 4500 homes in Mill Valley and all of them recycle plastic. If
    each household recycles 10 soda bottles a day and buys one polar fleece
    pullover per month, does Mill Valley have a monthly plastic surplus or
    deficit? Bonus question: Assuming all the plastic bottles are 1 liter size,
    how much Evian are they drinking?

    9). If the average person can eat one pork pot sticker in 30 seconds, and
    the waitress brings a platter of 12 pot stickers, how long will it take
    five vegans to not eat them?

    10). Todd begins walking down Market Street with 12 $1 bills in his wallet.
    If he always gives panhandlers a single buck, how many legs did he have to
    step over if he has $3 left when he reaches the other end and met only one
    double-amputee?

    Advanced Placement Students Only

    11) Katie, Trip, Ling, John-John and Effie share a three-bedroom apartment
    on Guerrero for $2400 a month. Effie and Trip can share one bedroom, but
    the other three need their own rooms with separate ISDN lines to run their
    web servers. None of them wants to use the futon in the living room as a
    bed, and they each want to save $650 in three months to attend Burning
    Man. What is their best option?

    a) All five roommates accept a $12/hour job-share as handgun monitors at
    Mission High.
    b) Ask Miles, the bisexual auto mechanic, to share Effie and Trip's bedroom
    for $500/month.
    c) Petition the Board of Supervisors to advance Ling her annual
    digital-artists-of-color stipend.
    d) Rent strike.

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    From: david.springthorpe@REMOVEidx.com.au (David Springthorpe)

    Something to offend nearly every ethnic group :

            BANKSTOWN HIGH  SCHOOL

                 CITY OF  BANKSTOWN

                 MATHEMATICS EXAM

    NAME  ............................

    GANG  ............................

    Time allowed 1 hour

    If  Mohamed lowers his WRX 2 inches front and back and puts on stolen
    18-inch Zepter wheels, how many inches has he originally lost from the
    stock suspension?

    If Con needs 3 razors a day to stay clean shaved,  how many razors will he
    need before he goes to the gym at  8.00pm?

    If Mustaffa runs 10 km from the Police in Lakemba to Punchbowl  then steals
    a car and drives another 5 km to Bankstown, how  many kilometres has he
    travelled if he ends up hiding in Wiley  Park?

    Omar has 2 ounces of cocaine and he sells an "8 ball" to Hamil  for $320.00
    and 2 grams to Akhmed for $85.00 per gram, what is  the street value of the
    balance of the cocaine if he doesn't cut  it?

    If Ahmed receives $200.00 per week disability allowance  from Centrelink and
    works for his brother as a builder and  receives a further $400.00 per week
    and then pays $10.00 per week  for each of his 11 children for school, how
    much money does he  have left to buy a smashed Tarago from the auctions?

    If the average spray  can covers 22 square metres and the  average letter is
    8 square centimetres, how many letters can a tagger spray with 3 cans of
    paint?

    If Soula needs 25 mls of wax  per day to get rid of her facial hair and
    Soula is only 19 years  old, how many mls will her mother need if she is 47?

    Mohamed has an AK-47 with 2 x 30 round clips. If he misses 6 out of  10
    shots and shoots 13 times at each drive-by shooting, how many  drive-by
    shootings can he attend before he has to  reload?

    If Jim changes the oil in his Fish & Chips shop deep fryer every  18 months
    and this costs him $400.00, how often should he change  the oil if he wants
    to spend only $180.00 per annum on new  oil?

    If Abdo runs a Donor Kebab shop and works as a Taxi driver on  weekends and
    earns $1,200.00 per week, how much does Centrelink  give him for his job
    search allowance?

    If Bankstown's ethnic  community is increasing at a rate of 3.5% per month,
    the overall  population increasing at 2.1 % per month, at what rate are  the
    Aussies leaving?

    Nabil wants to cut his 8 ounces of heroin  to make a 20% profit, how many
    ounces of cut will he  need?

    Chang gets $200.00 for stealing a BMW, $150.00 for a Commodore  and $100.00
    for a Falcon. If he has stolen two BMW's and three  Falcons, how many
    Commodores will he have to steal to make  $1,800.00?

    If Bilal gets a haircut and gets a number 2 on the sides and a  number 3 on
    top, then goes back 3 weeks later and gets a number 1  all round, how much
    has his hair grown in 3 weeks? (Assume that  his hair grows evenly at a rate
    of 2 mm per day)

    Quang is pimping for three girls. If the price is $75.00 for  the trick, how
    many tricks will each girl have to turn so  that Quang can pay for his $200
    per day crack habit?

    If  Greg Smith hears the word "yullah" approximately 55 times per  hour in
    Bankstown Square, How many times will he hear the word "mate"  in Penrith
    Plaza, if Bankstown has a population of 85,000 and  Penrith has a population
    of 10,000?

    If Luigi drives his family  and cousins all in one car from Leichardt to
    Stanmore, how many round  trips will he need to make if 40 of his relatives
    need a lift and  he can put 12 people in his Valiant at any one given time?

    If Ahmed uses  1 kg of "bog" to fix his smashed car, how many cans  of spray
    paint will he need if Hardware House is selling them for  $9.00 each and
    each can has 85 mls and the ambient air  temperature averages at 22.5
    degrees Celsius?

    Trinh is in prison for  6 years for murder. He received $10,00.00 for the
    hit.  His  common law wife is spending $100.00 per month. How much money
    will be left when he gets out of prison and how many years will  he get for
    killing the bitch that spent his money?

    If  Mario's dad has his top 3 buttons of his shirt open and reveals 1 x
    golden cross  and 2 other golden ornaments, and has approximately 17 sq cm
    of hair coming from  his chest with an average length of 2 cm, what is the
    probability that the  ornaments will be visible from:

    2 feet away .....%

    5 feet away  .....%

    100 feet away  .....%

    If Effie's mum sells her galaktoboureko for $2.00 per slice and  she wants
    to make an extra 10% profit on each slice, how many sheets of filo  pastry
    will she leave out if the filo pastry costs 62 c a sheet and she normally
    uses 17 sheets on each tray which she cuts into 16 slices?

    Hamul has  knocked up 6 girls in his gang. There are 27 girls in the gang.
    What percentage  of the girls in the gang has Hamul knocked up?

    If George has $12,000.00  and buys 2 smashed cars from the auctions, how
    much will it cost him to fix them  if his friend from school Ahmed is a
    panel beater and charges him Habib rates of  $40.00 per hour?

    If Layla has to move her eyes 50 degrees to the right  when doing her maths
    HSC exam to see Julie Wilson's answers, how many degrees  will she have to
    move her head if Michelle, Linda and Lisa are sitting 1  metre apart from
    Julie?

    D.S.

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    From: Kurt Jaeger <jaegerk@cae.wisc.edu>

One of my undergrad professors was asked what kind of of problems would be on the final. His answer: "Just study the old tests. The problems will be be the same, just the numbers will be different. But not all the numbers will be different. Pi will be the same. Planck's constant will be the same... "

Another professor, when asked how many problems there would be on the final, turned to the student and replied, "I think you will have lots of problems on the final."

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    From: Peter Taylor <P.A.Taylor@open.ac.uk>
    This isn't really a joke, it supposedly happened in a UK GCSE exam some
    years ago, but it may amuse you:

    question: how many times can you subtract 7 from 83, and what is left
    afterwards?
    answer: I can subtract it as many times as I want, and it leaves 76 every
    time.

mathematics
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    From:   Jonathan W. Hoyle <jhoyle1@rochester.rr.com>
    I don't know of that one.  But when I was an undergrad, one of my
    professors told me that when he was a student, and he had trouble with a
    proof trying to get past step n to step n+1, he would always start with
    "Clearly ..."  Although, he said, he'd get a few points off for "needing
    more detail at this step", his professor thought that he knew what he
    had to do, so he'd largely get away with it.

    He also informed us that because he knew the trick, he was not likely to
    be fooled if we tried to pull that stunt.  :-)

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    From:   William L. Bahn <bahn@bfe.com>
    I think the one you might be referring to shows a proof that starts at the
    beginning and goes partway. It then picks up again and proceeds to the end.
    In the middle between the two parts is a something like, => Then a miracle
    occurs =>

    The professor, looking at the proof, comments, "You need to be a little more
    explicit here in step two."

    Once, when I was grading an exam, I got a paper that had the right answer to
    four sig figs. But the problem had been set up incorrectly from the very
    first line. I was therefore all geared up to ream this student a new one for
    cheating - or for the very least for employing "magical methods" which is
    quite common when the answers to a problem are in the back of the book.

    As I worked through this student's work, it turned out that they had made
    three separate errors - they had set the problem up completely wrong. They
    had taken a quantity from one side of the equation to the other and didn't
    flip the sign and they had added to fractions over different denominators by
    simply adding the denominators. The last two math blunders are common
    mistakes (and I firmly believe that the level of skill necessary to walk the
    correct answer back to the initial work and tie it in through the use of
    these devices was way beyond this student's reach). But, it turned out that
    that the combination of the three unrelated errors just happen to yield the
    right answer to four sig figs.

    While I found this very intriguing and interesting, I graded the problem
    just as though the answer had only been close. But I did layout this
    peculiar coincidence to the entire class. I was surprised by the number of
    students that truly felt that the guy should have received full credit for
    the problem since, "Why should it matter HOW the answer is arrived at, as
    long as it's correct." BTW: The guy whose paper it was agreed that the
    answer deserved no more credit than any incorrect result.

    The guy that was the most vocal about how unfair this was wouldn't let it
    go, so I asked him, "Let's say you went to a doctor with a certain ailment
    and he gave you a prescription and you took it and got better. You then
    found out that he had misdiagnosed your ailment completely. He looked up the
    treatment in the Physician's Desk Reference, but read the wrong line from
    the index and so turned to yet another ailment in the book. When writing the
    prescription he then transposed some numbers in the dosage. The end result,
    purely by coincidence, it that you got a prescription for the right medicine
    in the right dosage and everything worked. Would you be eager to give that
    doctor full credit and go back to him again? Or would you say, "I'm sure
    happy that you got lucky, but your license to practice should be yanked
    immediately."

mathematics
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    From:   Daniel Giaimo <dgiaimo@nospam.ix.netcom.com>
        Another version I've heard is that when the student gets the paper back he
    sees a -1 on that problem which has been crossed out.  A note on the back
    explains that the grader at first didn't think that this step was obvious, but
    after thinking about it for an hour, decided that it was.

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    From:   Hauke Reddmann
    One student was stuck and wrote: The proof of this is
    left as an exercise for the reader.
    The prof wrote: Did it, fell for a non sequitur and made a
    minor calculation error. You get a B+.

mathematics
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                                   EXAM HOWLERS

    From: Wade Ramey <wrameyxiii@home.remove13.com>
    Problem: Find the limit of [sin(7x)]/(5x) as x -> 0.
    Actual answer from actual student: [sin(70)]/(50).

    From: Dave L. Renfro <renfrod@central.edu>
    Once, in a "math appreciation" course, part of a test I gave
    had some one-variable linear equations to solve. Most of this
    course was "algebra-free" since many of the students had very
    weak backgrounds in math. However, solving one-variable linear
    equations was one of the topics covered and this test was
    given after that topic had been covered.

    Question -- Solve for x:  3x - 2 = x.

    Student asks during test -- "I can solve for x on the left side,
    but what do I do with the x on the right side?"

    From: "denis-feldmann" <denis-feldmann@wanadoo.fr>
    Similar one: "Let S =1+1/4+1/16+...+1/4^n; calculate 4S and deduce the value
    of S "(this was written on the blackboard)
    Later, I heard a voice in the back of the room muttering to herself 'Mmm,
    ok,  I have calculated forty-five; what do I do now"?
     It took me a few minutes to understand :-)

    From: Brandon Hombs <hombs@ecn.purdue.edu>

    As a freshmem in college some of my friends had to take a trigonometry
    refresher course before they could proceed to calculus.  On one of the
    exams the students were asked what sin(x)/cos(x) equaled.  Obviously the
    professor expected, tan(x).  However, one student put:
    sin(x)/cos(x) =3D in/co

    How do you respond to an answer like that?!?

    From: kovarik@mcmail.cis.McMaster.CA (Zdislav V. Kovarik)

    My favorite variation:

    sin x
    ----- = six
      n

    In a first year linear algebra course for "applied" programs, one of the
    questions (on linear combinations) was to determine the ratio of mixing two
    solutions of sulphuric acid to obtain an intermediate concentration. One
    student protested that this was a chemistry question, and his program was
    economics.

    From: hutching@cartan.Stanford.EDU (Michael Hutchings)

    Once I saw the following.  A student was asked to prove that sets A and B
    are disjoint.  The student first proved that A is disjoint, then proved
    that B is disjoint, then concluded that A and B are disjoint.

    From: landsbur@troi.cc.rochester.edu (Steven E. Landsburg)

    I asked "Is there a smallest positive real number.  Why or why not?"

    A student wrote:  "There is no smallest positive real number, because
    if you thought you had found the smallest positive real number, you
    could divide it in half a get a smaller one."

    Full credit.  But he went on:

    "Then you can take the result of that calculation, divide it in half
    and get still a smaller one.  Then you can divide in half again to get
    something still smaller.  Then you can do it again.  This process
    generates a sequence that goes on forever.  It is infantile."

    From: Kristin Hein <kristinhein@home.com>
    This isn't as great but one of the students in my first year calculus
    labs answer the following on the quiz:

    Q:"find the limit as x approaches 3 of 6+3pi"
    A: 6+3(3) =12
    they substituted 3 in for pi, not knowing it was a constant.

    From: Kristin Hein <kristinhein@home.com>
    Date: Thu, 15 Mar 2001 22:04:34 GMT

    This isn't as great but one of the students in my first year calculus
    labs answer the following on the quiz:

    Q:"find the limit as x approaches 3 of 6+3pi"
    A: 6+3(3) =12
    they substituted 3 in for pi, not knowing it was a constant.

mathematics
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    From: "William Heierman" <wheierman@corunduminium.com>

    It is a whimsical story about my alter ego and how he got his "A" in
    Calculus by convincing his instructor that he had found a remarkable new
    integration principle:  the integral of a product is the product of the
    integrals.  As a teacher of calculus, I found this approach often used by
    students at sea when it came to such antiderivatives; and I wondered if it
    could ever produce a correct result.  Surprisingly, it could; and I was able
    to find both general existence properties and fruitful constructive methods.
    Some of the results and outlines of proof can be found in my string,
    "Integrals of Products are Products of Integrals" in the "news:sci.math"
    Discussion Group of the "Mathforum" site.

    Beginning with the professor duly skeptical, Bill uses examples to parry
    every attempt by the professor to poke holes in his assertion; until finally
    the professor himself is convinced it is indeed true!  Because the text is
    symbolically complex (some of the functions are quite tedious), I refuse to
    type the examples; but I can send you a photocopy of my manuscript if you
    are interested and will tell me your regular mail address (in The
    Netherlands?).

    Most of my colleagues who have seen it think it is pretty funny.  It is also
    entertaining to work out the examples using the "legitimate" methods of
    calculus (and not avoiding the issue by differentiating the right hand
    sides)!  I would have a second person check the results (just in case I
    wrote an error) before publication, however.

next page | Index | Comments and Contributions

#### Subsections

- 1. mathematics - general
- 1.1 proofs
- 1.2 statistics and statisticians
- 1.3 mathematicians
- 1.4 mathematics poetry
- 1.5 mathematics quotes
- 1.6 mathematic puns
- 1.7 mathematical terms
- 1.8 mathematical exams
- 1.9 learning mathematics
- 1.10 mathematical tests to take
- 1.11 mathematical equations
- 1.12 topology
- 1.13 numbers
- 1.14 set theory
- 1.15 functions

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