Math Problems!........share It Here!

[Jourdan]

Pag sa calculator o computer, and sagot ay "ERROR".

 

Pero kung pag-aaralan, ang sagot dapat ay INFINITY, except kung Zero yung ididivide.

 

Kung Zero yung ididivide, zero and sagot.

wrong...

 

a zero divided by a zero IS NOT = 1 AND NOT also = 0

 

it is an indeterminate form...

 

rational terms resulting to a zero divided by zero can be evaluated using L'Hopital's Rule.

Edited September 29, 2004 by Jourdan

[Jourdan]

on dividing by zero:

 

to divide by a number x is to multiply by its multiplicative inverse, 1/x

 

the reciprocal/inverse of a number is that which when multiplied by the number is 1

 

so we need the value of 1/x when x=0. however, any number multiplied by zero is zero (zero property of multiplication).

 

and so zero has no inverse, and we can't divide anything by it. ganun na yun, parang langis at tubig na di maghahalo kahit ano pa ang bate mo.

 

 

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

 

regarding the lotto, let us simplify the game first. hulaan ng labas sa six-sided die, tapos tatlo lang tao sa mundo na tag-isa ang mga hula. kumbaga 1-6 ang laro.

 

chances of winning? 1/6, for each player

 

chances of no person winning: (5/6)(5/6)(5/6) = 125/216

chances of exactly 1 person winning: 3(1/6)(5/6)(5/6) = 75/216

chances of exactly 2 persons winning: 3(1/6)(1/6)(5/6) = 15/216

chances of all persons winning: (1/6)(1/6)(1/6) = 1/216

total probability: 1 (125+75+15+1=216)

 

the point of it all: least likely scenario is that everyone wins, least likely is no one wins, with other possiblities falling inbetween. pero di masasagot yang lotto question kung walang assumption kung ilan ang tumaya, kung ilang numero ang tinaya ng mga tao, kung nandadaya ba yung mga taga-PCSO, etc.

 

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

 

i move that this thread be closed!

wrong on division by zero.

 

rational terms involving a 0/0 at some x = a is not uncommon....The limit of that rational term at that point is easily obtained by L'Hopital's rule.

 

and any polynomial expression which will not reduce to 0 for all values of x when divided by 0 will result to infinity, positive or negative depending on the value of the polynomial expression...

 

 

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

 

wrong on statistics of lotto.

 

probabilities of winning are INDEPENDENT of the number of bettors. these are dependent ONLY on 2 things:

a. no. of numbers to choose from

b. no. of numbers that would make a bet.

 

it is the AMOUNT OF MONEY or POT that is dependent on the number of bettors...

 

usually, lottery bodies have an automated system to adjust winnings depending on the bets collected...

[boy男孩]

wrong on division by zero.

 

rational terms involving a 0/0 at some x = a is not uncommon....The limit of that rational term at that point is easily obtained by L'Hopital's rule.

 

and any polynomial expression which will not reduce to 0 for all values of x when divided by 0 will result to infinity, positive or negative depending on the value of the polynomial expression...

 

 

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

 

wrong on statistics of lotto.

 

probabilities of winning are INDEPENDENT of the number of bettors. these are dependent ONLY on 2 things:

a. no. of numbers to choose from

b. no. of numbers that would make a bet.

 

it is the AMOUNT OF MONEY or POT that is dependent on the number of bettors...

 

usually, lottery bodies have an automated system to adjust winnings depending on the bets collected...

hmmn. i think i got some back up here.

[quintix]

my answers differ because i see the question differently, not because i use different mathematics.

 

the original question of dividing by zero for me is a question of algebra, not of calculus... and so i used the axioms of algebra to demonstrate why it is not allowed. this is the more fundamental approach to this question.

 

the evaluation of rational expressions or functions at a point of discontinuity is a different matter in my view. even if the denominator happens to be zero, or evaluates at zero.

 

 

as for the probability question, i was exploring the odds of X=n where X is the number of lotto winners in a draw and n>1. In this case, the number of bettors is indeed a factor. the assertion of only two factors being relevant is for the case of X=1.

 

 

i moved to close the thread but such motion was not carried and seconded, not to mention we all fully realize such declaration would not actually close the thread.

 

and finally i used the analogy of oil and water to stress a point, in that dividing by zero cannot have an answer.

[dyakhardy]

d yata ako pwede dito, chismis na nga lang hheehe.. daan lang po.. hi peeps!

[howard_the_duck]

And i move that this thread should not be closed!

Marami palang matututunan dito e...

One question: may simple formula ba ng paghahanap ng mga prime numbers? (Sorry kung natanong na.... thanks...)

[Jourdan]

my answers differ because i see the question differently, not because i use different mathematics.

 

the original question of dividing by zero for me is a question of algebra, not of calculus...  and so i used the axioms of algebra to demonstrate why it is not allowed. this is the more fundamental approach to this question.

 

the evaluation of rational expressions or functions at a point of discontinuity is a different matter in my view. even if the denominator happens to be zero, or evaluates at zero.

as for the probability question, i was exploring the odds of X=n where X is the number of lotto winners in a draw and n>1. In this case, the number of bettors is indeed a factor. the assertion of only two factors being relevant is for the case of X=1.

i moved to close the thread but such motion was not carried and seconded, not to mention we all fully realize such declaration would not actually close the thread.

 

and finally i used the analogy of oil and water to stress a point, in that dividing by zero cannot have an answer.

<{POST_SNAPBACK}>

 

on division by zero:

 

do not blur algebra and calculus...they aren't different. for one, any constant is undeniably a polynomial expression with all coefficients of x equal to 0, e.g., 2 = 0x^2 + 0x^1 + 2.

 

To generalize, any WHOLE NO. or INTEGER is a polynomial term.

 

It is thus prudent to evaluate a general question using polynomial expressions...a general solution to cater to a general question...a general solution that is true for all polynomial expressions of x, where x is an element of Real Nos.

 

note that ur analogy IS NOT BASED ON any mathematical theorem. it is your own invention...and a stupid one.

 

 

on winning probabilities:

 

even if there's only one bettor, his chance of winning the lottery does not change...his bet will still have to compete will all the possible 6/42 combinations...

 

perhaps u r just confused...the lottery body's chance of "winning" is the one that is dependent on the number of bets...the more bets, the less chance the lottery body "winning" the lottery...this lottery body's chance of "winning" is none other than the sum of the probabilities of each bettor losing (cumulative probability of ALL bettors losing).

 

ex. if there's only one bet, the chance that the bettor will win is 1 of 42C6, the chance he will NOT WIN is (42C6 - 1)/42C6 ,w/c is the chance the lottery body will "win".

 

if there will be 2 bets, the lottery body's chance of "winning" (or ALL bettors losing) will then be (42C6 - 2)/42C6 ...lower than when there is just one bettor.

 

i hope this will now be clear to you.

[quintix]

hahahahahaha..... oh my God salamat sa iyo

 

 

a beam of light has broken through the darkness...

 

it is all so clear now: i should no longer bother with this thread.

 

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

 

happy discussions... sana marami kayong matutunan!

[floppydrive]

rational terms resulting to a zero divided by zero can be evaluated using L'Hopital's Rule.

<{POST_SNAPBACK}>

 

 

Could you refresh our memory on L'Hopital's rule? Na-atrophy na yata yun sa utak ko.

[The_Blade]

Could you refresh our memory on L'Hopital's rule?  Na-atrophy na yata yun sa utak ko. 

<{POST_SNAPBACK}>

 

 

TAAS KO LANG.

[Stoecker]

get the derivatives of the upper and lower terms of the limit. if the result is another indeterminate (infinity/infinity, 0/0) then do it again.

 

 

Could you refresh our memory on L'Hopital's rule?  Na-atrophy na yata yun sa utak ko. 

<{POST_SNAPBACK}>

[strong_cock]

What is the value of 1/1+1/8+1/27+1/64+1/125+...?

The nth term is the reciprocal of n^3.

If 3 is replaced by 2, it is known that the series sums to (pi^2)/6.

If 3 is replaced by 4, it is known that the series sums to (pi^4)/90.

[The_Blade]

What is the value of 1/1+1/8+1/27+1/64+1/125+...?

The nth term is the reciprocal of n^3.

If 3 is replaced by 2, it is known that the series sums to (pi^2)/6.

If 3 is replaced by 4, it is known that the series sums to (pi^4)/90.

<{POST_SNAPBACK}>

 

 

it converges to 1.20205690315031

 

 

 

Why is 0! = 1. How do you prove this?

[gineh]

get the derivatives of the upper and lower terms of the limit.  if the result is another indeterminate (infinity/infinity, 0/0) then do it again.

<{POST_SNAPBACK}>

 

may value ka ngang makukuha using l'hopitals rule but this would still not be a rational answer to numberdividedbyzero.

 

lhopitals rule gives the answer for limit of a ratio as it approaches a number s.t. the denominator approaches zero as it approaches said number.

[gineh]

One question: may simple formula ba ng paghahanap ng mga prime numbers? (Sorry kung natanong na.... thanks...)

 

so far, walang alam. pero i think finding a pattern or as you said, a formula is one of the key problems in theoretical mathematics today.

 

pero may "common" prime number of the form [(2^n)-1]. may university nga na nag o-offer ng cash prize ($50,00 ata) sa kahit sinong makahanap ng bagong prime of that form.(pero syempre, trabaho mo nang patunayang prime yun, latest one found was something like 50 digits long.

 

and kung gusto nyo din talagang karirin ang math problems, try nyong subukan tong problems na to, solve one and win ONE MILLION DOLLARS! lupet no? pero in the 5 years that these problems have been published, only 1 out of 7 have been solved.

 

Clay Institute of Math Millenium Problems

 

eto sample ng isa:

 

Yang-Mills and Mass Gap

 

The laws of quantum physics stand to the world of elementary particles in the way that Newton's laws of classical mechanics stand to the macroscopic world. Almost half a century ago, Yang and Mills introduced a remarkable new framework to describe elementary particles using structures that also occur in geometry. Quantum Yang-Mills theory is now the foundation of most of elementary particle theory, and its predictions have been tested at many experimental laboratories, but its mathematical foundation is still unclear. The successful use of Yang-Mills theory to describe the strong interactions of elementary particles depends on a subtle quantum mechanical property called the "mass gap:" the quantum particles have positive masses, even though the classical waves travel at the speed of light. This property has been discovered by physicists from experiment and confirmed by computer simulations, but it still has not been understood from a theoretical point of view. Progress in establishing the existence of the Yang-Mills theory and a mass gap and will require the introduction of fundamental new ideas both in physics and in mathematics.

 

ano? kaya ba?