why is the division of any number by zero is impossible?
595633
When you are dividing by something you are trying to find out how many of a certain amount (say, 3) is in another amount (say, 12). The result for my example, is of course 4, since 3 goes into the number 12 four times.\n\nNow the number 0 is nothing, literally. So if you're dividing into, say 12, you're wondering how much nothing is in 12. That's just not possible, because 12 is all "something".\n\nI hope that's clear enough...I tried.\n\nEdit: The guy above me is wrong.
680886
You can't because it does!\n\nFirst assume x = 0.999... repeating\n\nx = 0.999...\nx = 0.333... + 0.333... + 0.333...\nx = 1/3 + 1/3 + 1/3\nx = 3/3\nx = 1\n\nSo 0.999... = 1\n\nThis is a valid proof with no faulty logic, division by zero etc.\n\n0.999... *does* equal 1\n\nAnother way to prove this is as follows:\n\nx = 0.999....\n10x = 9.999...\n10x - x = 9.999... - 0.999...\n9x = 9\nx = 1\n\nFor the person that says subtract from 1 and you get 0.0000000001, you don't.  You have to have an infinite number of zeros, not a finite set.  You could write this number as 10^-n where n = infinity.  This is also 1 / 10^n where n = infinity.  The lim as n->infinity of 10^-n is zero, similarly the lim as n->infinity of 1 / 10^n is also zero.  So you are adding zero.  This therefore another proof that 0.999... *equals* 1.\n\nAnd if you *still* don't believe me, read the Wikipedia entry below.
1102494
0/0 is a discontinuity.\n\nIt is not specifically defined in the axioms of normal arithmetics. but, you can modify any set of axioms according to your own need, as long as they remain consistent and do not self contradict. U can define 0/0 to be 0, or u can define it to be 1 or 2 or 3... but before u proceed ahead, u have to make sure, by defining it as 1, your axioms do not self contradict. say,\n\n0/0=1\n\nwhat is (0/0) x0?\n\nif normal arithmetical rules apply... that (a/b)c=(ac)/b\n\n(0/0)x0=1x0=0\n(0x0)/0=0/0=1\n\nby setting 0/0=1, it contradict one of the rules, (a/b)c=(ac)/b, hence, in light of the original axioms, u cannot have 0/0=1.\n\nThe point is... as long as other rules r not broken, u can add definitions to mathematical objects to create a new object. U can still define 0/0=1, and change the (a/b)c=(ac)/b rule. u then have to make sure by removing this, other contradictions don't arise. Or u can set a rule saying, (a/b)c=(ac)/b applies except when (0/0)x0. again, u gotta check for contradictions. u can adjust everything until finally u have a new mathematical object that is wholly consistent with 0/0=1. Then, with this object, 0/0 is defined. Now, however, this new object would not behave like the ordinary number field we r familiar with.
1137443
It's undefined.  You can't divide any number by 0.
164065
The trick with "proofs" like these are generally an obscured division by zero. One of the lines seems to work, though when you divide to cancel out some factors, the quantity you're dividing by could/does equal zero. It's a trick and doesn't say anything substantial about mathematics.
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.
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.
337736
Its because strictly speaking c*b is NOT defined.\nWhy? Multiplication is Not defined for a number with infinite decimals, ie, c = 3.3333...\n\nThis is an old trick I used before.\n\nI'll prove to you that \n1 = 0.999... (the 9's goes on forever ) you can try it. \nLet y = 0.999 ... (1) \nNow multiply both sides by 10 to get,\n  10y = 9.999 ... (2) \nNow (2) - (1), gives us, \n   9y = 9 or \n    y = 1 \n\nbut in the begining we assumed that y = 0.999... \nand thus we have proved that 1 = 0.999... \n\nThe answer is we cannot multiply or divide numbers with infinity of digits by our usual way of definition. \n\nNevertheless, we use the "techniques" above a lot in approximation for example, the sum to infinity of a geometric series with common ratio less than 1.\n\nCertain rational numbers allow their decimal representation repeat in a pattern. Like above, after the decimal point, the pattern is "3". Rational numbers are numbers of the form p/q, where both p and q are integers.\n\nOther example is 56/11 = 5.090909... where the repeating pattern after the decimal point is "09".\n\nWorking backwards, one can show that the number \nm = 5.090909...(1) is actually a rational number. \nConsider, 100m = 100* 5.090909... \n               =  509.090909...(2)\n\n(2) - (1), gives us,\n \n   100m - m  = 509.090909... - 5.090909...\n        99 m = 509 - 5 = 504\n\nand thus, m = 504/99 = 56/11 done.\n\nA careful observer may ask, the two "methods" look the same! How come in proving the former ( 1=0.999... ) this "method" is considered wrong while in proving the latter ( 56/11 = 5.090909... ) the method is viewed acceptable? I cant answer that with absolute certainity. I dont think anyone can. Thats where the mystery is. And I am a mathematics student.\n\nAfter some thought, I conclude that one possible reason is because of the idea of writing 56/11 as 5.090909... is "created" by us. The idea of "rewriting a fraction in decimal form". And the weirdness is due to the varying effects of the concept of "infinity". In some cases, "inifinity" can mean this when a mathematical operation is done on it, while on others it may mean that...\n\nWell, all this a product of human thought.\nIt shows the frailty of the human defined concept.\n\nRegards.
955822
a+b-c=0\nDivision by a+b-c is division by zero, an "illegal" operation.\n\nI think that the "proof" is saying that the only way to make the process true is if a+b=0.  The "proof" stands apart from the assignment of values (a=4000, b=6000).
802753
"Division by Zero in mathematics is undefined because no definite meaning can be attached to this operation. To understand this, notice that a/0=b must (if it means anything) mean the same as a=0•b.\nHowever, if a≠0 then a=0•b is not true for any b; and if a=0 then a=0 is true for every b. This tells us that a/0 cannot be assigned a definite value- and therefore has no meaning."    --George Simmons
197247
its impossible because there needs to be either one less sign or one more number look:\n\nin a the order:\n2 * 4 - 6 + 8 /\n              ^there is an extra sign!!
103215
With this given data, it is not possible\n\nalthough the area is totalling to be 70 for both cases (7*10 and two pieces of 8*8 + 1*6) but with one division only, this is not possible\n\nPLEASE DO LET ME KNOW IF THERE IS SOME SOLUTION (i found it very interesting)
238636
It is impossible to have 0 as a denominator.
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...
305609
Division by zero is not allowed.\nSet the denominator equal to zero and solve for x.\nx^2 - 9 = 0\ngives x = -3 and x = 3.\nThus, the domain is\nAll real numbers except -3 and 3.
761771
It isn't.  Zero divided by zero is a non-defined number.
416203
You divide by 0 when you divide by a-b