What is actually meant by dividing a quantity by zero?
153279
Zero (0) is a paradoxical number that has high philosophical and scientific importance. Context of zero in absolute & applied Mathematics is different. In applied mathematics we use it according to our convenience, for example 0 degree celsius, 0!(factorial), initial Velocity, initial position etc. And in Absolute Mathematics we think of it transcendently. Absolute zero is beyond our experience.Therefore we are using and thinking of zero in diffrent context. \nIn the fraction a/o, at present the numerator `a' is considered as something that is considerable. And the denominator `0' is not used in the absolute sense insted it  is taken in the concept of `infinitesimally small'.That is the symbol `0' here stands for `infinatesimally small'.For instance a `point' is considered as magnitude and dimensionless which is relatively true and wrong in the absolute sense.\nContext a/0=a is also correct iff same meanig is strected all through. ie. a/0 implies `a' is `undivided'.Then a*0 means a is not at all multiplied, hence a*0=a only in the absolute sense. Here `a' which is the quotient and  the product is same to both expressions implies that `a' is individual and Independent.This concept is non-pragmatic hence not in use.\nMathematically,a=(1+1+1...`a' times).\nGeneraly, if a/m =n, a=m*n = (m+m+m+...`n' times) \nAnd, if m is infinatesimally small,a=(m+m+m+... infinite  times).At present the parodoxical symbol `0' is used to denote the axiom `infintesimaly small'.consequently. it is written as a/0= `Infinity'\nNote that divisibility exists iff something exists in the denominator.And in the same way multiplicability exits iff something exits as multiplier.
604013
there is no answer becuase it is impossible to divide by 0
395828
haha, but this does not work. you cannot mathematically divide by (a-b) because this quantity is equal to 0. (1-1)=0. Dividing by zero yields an indeterminate answer.
997321
Division by 0 is undefined. \n\nIf you divide 4 by 2, you get 2. Reverse the process: 2 multiplied by 2 gives you 4.\n\nThe reason you can't divide by 0 is because you can't multiply 0 by any other number and get a number besides 0.\n\n4 divided by 0 gives you "undefined." That would mean that "undefined" times 0 should equal 4. But that's silly.
696843
Check MathForum.org:\n\nQuestion:\nWhat is the quantity 0^0 (zero to the zeroth power)?  Would it be \n0, since 0 times anything is 0, or would it be 1, since anything to the 0 power is 1?  Or is this undefined, too?\n\nAnswer:\nThis, too, is an indeterminate form.  Its logarithm is 0 * infinity.\n\nMore detail from the website:\nSay you wish to introduce a new element (or maybe two elements) infinity which you wish to append to the real number system.  That is not prohibited.  After all, that is how we got from natural numbers to integers (appending negative integers and zero), and from integers to rationals (appending ratios of integers), and from rationals to reals (appending limits of convergent sequences), and from reals to complexes (appending the square root of -1).  What you end up with is not the real number system, however.  Furthermore, if you wish to define the four operations + - * and / for this new system, you probably want them to be the same on real numbers, and just add on the definitions of things like infinity + r and r/infinity, for any real number r.  Some of these work fine.  It makes sense to define:\n\n        infinity + r = r + infinity = infinity\n  (-infinity) + r = r + (-infinity) = -infinity\n                infinity + infinity = infinity\n          (-infinity) + (-infinity) = -infinity\n                       infinity - r = infinity\n                    (-infinity) - r = -infinity\n                       r - infinity = -infinity\n                    r - (-infinity) = infinity\n             infinity - (-infinity) = infinity\n             (-infinity) - infinity = -infinity\n        infinity * r = r * infinity = infinity  for r > 0\n  (-infinity) * r = r * (-infinity) = -infinity  for r > 0\n        infinity * r = r * infinity = -infinity  for r < 0\n  (-infinity) * r = r * (-infinity) = infinity  for r < 0\n infinity * infinity = (-infinity) * (-infinity) = infinity\n infinity * (-infinity) = (-infinity) * infinity = -infinity\n                       infinity / r = infinity  for r > 0\n                    (-infinity) / r = -infinity  for r > 0\n                       infinity / r = -infinity  for r < 0\n                    (-infinity) / r = infinity  for r < 0\n                       r / infinity = 0\n                    r / (-infinity) = 0\n\nWhere we get into trouble is with defining the following:\n\n        infinity + (-infinity)\n     (-infinity) + infinity\n        infinity - infinity\n     (-infinity) - (-infinity)\n               0 * infinity\n        infinity * 0\n               0 * (-infinity)\n     (-infinity) * 0\n        infinity / infinity\n        infinity / (-infinity)\n     (-infinity) / infinity\n     (-infinity) / (-infinity)\n        infinity / 0 = infinity\n    (-infinity) / 0 = -infinity\n\nThese expressions are called "indeterminate forms."  These can all have a large range of different values, depending on exactly where the "infinity" parts came from.\n\nAs a result, the system you construct is not closed under addition, subtraction, multiplication, or division.\n\nOther indeterminate forms are 0^0 and 1^infinity.\n\nSo the answer, is 0^0 is undefined or indeterminate.
15686
Division by zero is an operation for which you cannot find an answer, so it is disallowed. You can understand why if you think about how division and multiplication are related.\n\n   12 divided by 6 is 2   because\n    6 times 2 is 12\n\n   12 divided by 0 is x   would mean that\n    0 times x = 12\n\nBut no value would work for x because 0 times any number is 0. So division by zero doesn't work.
387091
Actually your question is the explaination of division operation of the number 1000000 to the number 0...\nThere is infinite zeros at any Real number... The number of a million is allready a Real number... Then we can say that the answer is infinite... Even if you like to ask another Real number the answer doesn't change... It is infinite for all Real number...
395566
1...anything multiplied by 1 is itself...so in division anything divided by itself is 1
572082
There are many undetermined ( not undefined ) mathematical quantities such as :\ninfinity - infinity\ninfinity / infinity\nzero / zero\nzero ^ zero\nzero * infinity\nas an example : (0^2)^0 = 0^0\n                (0^3)^0 = 0^0\nis that mean that 2=3 ?\nSo 0^0 is an undetermined quantity\nregarding that zero can be considered as the smallest +ve quantity we can ever have or the biggest -ve quantity we can ever have
540459
something close to zero
676991
Schools should teach that you can't divide by zero. 20/0 is an insolvable problem. 0/20 is 0.
750843
you cannot divide by 0 = a-b\n&#92;
484386
0 as a number\n\n0 is the integer that precedes the positive 1, and follows −1. Zero first appeared as a number in Brahmagupta's work dated to 628. Prior to that Babylonians used a space marker that played one of the functions of zero. Babylonians did not have a special symbol for zero. In most (if not all) numerical systems, 0 was identified before the idea of 'negative integers' was accepted.\n\nZero is an integer which quantifies a count or an amount of null size; that is, if the number of your brothers is zero, that means the same thing as having no brothers, and if something has a weight of zero, it has no weight. If the difference between the number of pieces in two piles is zero, it means the two piles have an equal number of pieces. Before counting starts, the result can be assumed to be zero; that is the number of items counted before you count the first item and counting the first item brings the result to one. And if there are no items to be counted, zero remains the final result.\n\nWhile mathematicians all accept zero as a number, some others would say that zero is not a number, arguing one cannot have zero of something. Others hold that if you have zero dollars in your bank account, you have a specific quantity of money in your account, namely none. It is that latter view which is accepted by mathematicians and most others.\n\nAlmost all historians omit the year zero from the proleptic Gregorian and Julian calendars, but astronomers include it in these same calendars. However, the phrase Year Zero may be used to describe any event considered so significant that it virtually starts a new time reckoning.\n\n\n\n0 as a numeral\n\nThe modern numeral 0 is normally written as a circle or (rounded) rectangle.\n\nOn the seven-segment displays of calculators, watches, etc., 0 is usually written with six line segments, though on some historical calculator models it was written with four line segments. This variant glyph has not caught on.\n\nEarly Europeans hesitated to consider zero as a numeral or number. Leonardo of Pisa or Fibonacci says the following in 1202 AD when the Indian number system arrived in Europe.\n\n"After my father's appointment by his homeland as state official in the customs house of Bugia for the Pisan merchants who thronged to it, he took charge; and in view of its future usefulness and convenience, had me in my boyhood come to him and there wanted me to devote myself to and be instructed in the study of calculation for some days. \nThere, following my introduction, as a consequence of marvelous instruction in the art, to the nine digits of the Hindus, the knowledge of the art very much appealed to me before all others, and for it I realized that all its aspects were studied in Egypt, Syria, Greece, Sicily, and Provence, with their varying methods; and at these places thereafter, while on business.\n\nI pursued my study in depth and learned the give-and-take of disputation. But all this even, and the algorism, as well as the art of Pythagoras, I considered as almost a mistake in respect to the method of the Hindus. (Modus Indorum). Therefore, embracing more stringently that method of the Hindus, and taking stricter pains in its study, while adding certain things from my own understanding and inserting also certain things from the niceties of Euclid's geometric art. I have striven to compose this book in its entirety as understandably as I could, dividing it into fifteen chapters.\n\nAlmost everything which I have introduced I have displayed with exact proof, in order that those further seeking this knowledge, with its pre-eminent method, might be instructed, and further, in order that the Latin people might not be discovered to be without it, as they have been up to now. If I have perchance omitted anything more or less proper or necessary, I beg indulgence, since there is no one who is blameless and utterly provident in all things."\n\nLeonardo of Pisa \nHere Leonardo
92491
OK, first off no one seemed to be able to answer the dividing by 0 and 1 issue correctly, so here goes...\n\nDivision by n is defined as multiplication by the multiplicative inverese of n.  The multiplicative inverse of n is defined as the number 1/n such that n*(1/n)=1.  Zero has no multiplicative inverse because 0 times anything is 0.  Therefore division by zero implies multiplication by a number that does not exist.  One does have a multiplicative inverse (1x1 = 1), so division by 1 is perfectly valid, although you are correct that the result is the number which was divided by 1.  It is exactly the same as multiplying by 1.\n\nNow on the area of a circle issue...\n\nYou seem to be trying to relate area to circumferance.  It's not hard.\nLet A = the area of the cirlce, c = the circumferance, and r = the radius.\nYou already know that A=(pi)r^2 and c=2(pi)r.\nSolve the second equation for r and get r=c/(2pi).\nNow substitute that into the first equation to get A=(pi)(c/(2pi))^2.\nThen simplify and you get A=(c^2)/(4pi).\n\nLike it or not, you can't get rid of the pi.  Pi is defined as the ratio of the diameter of a circle to its circumference, so it's going to be there no matter what.  When you say it's useless unless you know all the digits, this simply isn't true.  Depending on what you're doing, you can either get the pi's to cancel out, or you will be finding a decimal approximation of the area or circumference.  If the radius is a whole number, the area simply won't be (there may be a few values for which it will be, but most of the time it isn't), and any formula you come up with that says otherwise is incorrect.\n\nAs for the sphere question, I don't understand what you're asking.  Are you trying to equate area to volume?  They're not the same thing.  You can't find the area by sticking together infinitely thin slices as the slices have no height so you will never have a third dimension.  You might be able to do it using limits, but that's not going to be the kind of nice simple numbers you're looking for.  If you can explain what you meant, I might be able to do a bit better.
727687
Zero. Look at the top have of that division problem.
1006618
If you consider that density is defined as mass per unit volume, to claim that something has infinite density and zero mass is entirely false.  What I think you meant to say is infinite mass and infinitesimally small volume which would mean that density is infinite, too.\n\nHey, Jesse P.  I'm not sure if you were talking to me when you said that "because mass is zero infinite density is possible", but if that's the case, I was merely saying that to have zero mass would be impossible and make density non-existent.  There is no answer for density if mass=0 since mass is in the denominator and we know about dividing by zero.  Thus, it has to be infinitesimally small, but not zero.  I agree that it may be easier to understand conceptually to think of it as zero, but my point is valid.  I guess the absolutely accurate thing to say is that density has a limit of infinity as mass approaches zero.
89171
You cant just add or substract whatever is left. You invalidate the function of "division" by partially dividing then filling in the rest of the numerator. The number left over after something has been divided is called the modulo, and is useful for programming functions. You cant do an incomplete division(only dividing 20/5 instead of the 2/5 also) and then speculate as to why it cant be negative when doing a full division. It invalidates the definition.