Why when you divide anything with zero gives you infinity? Please prove with equations.?
487867
Here is the mathematical proof:\n\nIt involves some precalculus, so I will explain what I am doing just in case you haven't gotten to precalc yet.\n\n[1]  Definition: Limit\n     The limit of a function f(x) is the value of y @ x.\n     i.e. y = 2x^2, @ x = 1, y = 2, \n     Therefore, \n     limit 2x^2 = 2\n     x->1\n\n[2]  Why division by Zero = infinity:\n\n     limit 1/x = infinity\n     x -> +0\n\n     Limit 1/x = infinity\n     x -> -0\n\nThe graph of y = 1/x explains this principle. \n\n[2.1] Definition: +0  & -0\n\n+0 = As x approaches zero from the right.\n-0 = As x approaches zero from the left.\n\n[2.2] As x get closer and closer to zero, the quotient of 1/x gets larger and larger.\n\ni.e. 1/0.0000006 = 6000000\ni.e  1/1x10^-9999= 1x10^9999\n\n[2.3] When x becomes zero, the quotient of 1/x is infinity. Since infinity is underfined, 1/0 is also undefined!
820085
We say that division by zero is undefined, for it is not consistent with division by other numbers.\n\nHere's a little experiment for you to try on your calculator. Observe the output when you try the following set of calculations:\n       1/1\n       1/.1\n       1/.01\n       1/.001\n       1/.0001\n       1/.00001\n       etc... \n\nuntil your calculator can't go any further or you get tired. You should notice that the answers continue getting larger and larger. \nAnother way of thinking of it is to imagine filling a box with apples. Say a box can hold 100 apples. Now try filling it with apples that are half the size of these apples. You can put 200 in the box. Now imagine a special, magic apple that takes up no room at all. How many can you put in the box?\n\nWell, the answer is... there is no answer! That is why mathematicians refer to numbers that are divided by 0 as "undefined." Some people tend to think of them as being infinite, but this isn't exactly true. There simply is no answer.
127821
"Dividing by nothing" doesn't mean you would do nothing.  It means, "how many piles of nothing (zero) would you have to add up to get to the original number?".  \n\nHow many piles of zero would you have to have in order to have 2?  The answer isn't even infinity, because you would still never have 2.  So it's not possible, and 2/0 can't be represented by any number.
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...
238404
thanks 4 voting my answer as best but i didnt understand what u said\no divided by any no is always zero and with exception of zero where i guess it's not defined(aint that also zero iam not sure)
1127621
Actually the above "proof" is misleading. \n\nx=0.999...99\n\n10x=9.999...90 (as anything x10 adds a zero to the end as the decimal place shifts, even if the number is infinite)\n\n9x=10x-x\n=9.999...90-0.999...99\n=8.999...81\n\nx=9x/9=8.999...81/9=0.999...99\n\nTherefore 0.999...99 does not equal 1....mathematics isn't independent of logic. Beware of those who try to make it so.
448673
Forget about 1/0 and think a/b.  To ask "what is a divided by b?" is really asking (as Jethro would) "how many times does b go into a?"  Ask the question that way:  how many times does zero go into one?  Or how many nothings are in something?  Well, there are an infinite number of 'nothings' in anything, right?  You can always remove nothing from something and still have as many nothings left to pull out, and not change the original something at all.  So the answer to your question is 'infinity' which is not a number.
1165584
Thats a common misconception. \n limit x tends to 0,    5/x is infinity\nbut tends to 0 is not that x is equal to 0.It means x is almost 0(you are moving towards 0) but not 0.\nU cannot divide bu 0,its a undefined proposition.
608336
L'hopital's Rule does not apply in this case as the limit can be evaluated as it is, it is not one of the special cases which you would apply that (infinity / infinity, zero / zero).  Actually, if you did apply L'hopital's Rule, you would get the wrong answer (wrong answer being 1).\n\nIn this case, since as x approaches 3 (from either side), the numerator of the function goes to zero and the denominator goes to some finite, no zero quantity, you can just plug in 3 into the function and evaluate.\n\nThe limit of the function as x --> 3 = 0
90067
There's no answer actualy. O cannot be divided by 0. \nThe answer infinity is just an assumption when \nnumber really near to 0 divided by another number near to 0.\n\nSuch as 0.0000000000000000001 / 0.0000001\nAlthough the example doesn't really show number near to 0, but if you change to 0.00000000000000000....01, you will see the same result
890832
Gary, that's a good one, but one mistake...\nyou said that a=b, thus you cannot divide by (a-b) b/c that equals zero, and you cant divide by zero.
208997
The only way to get the expression infinity/-infinity is through a limiting process in the real numbers, so I'll assume you're talking about limits. In that case the form above is indeterminate, meaning that it depends on the functional forms in the limit. \nSuppose you have f(x) and g(x) such that lim [f(x)/g(x)] = infty/-infty. Consider the equivalent expression lim [f(x)/g(x)] = lim [(1/g(x))/(1/f(x))] which approaches the form 0/0. This allows the use of L'Hospital's rule to evaluate the limit, which we know from experience can be anything.
2944
The way you asked the question, you can't do it.  However, you can do something similar, and you don't always get infinity.  If you take a number, say 5, and divide it by (positive) numbers closer and closer to zero, you will get larger and larger numbers, and you can make the answer as large as you want by making the the denominator small enough.  For this problem you say that "the limit, as x approaches zero, of 5 divided x, is infinity."  You might say, 5 divided by zero is infinity for short, but that it isn't exactly correct.  \n\nNow here is another problem:  What is the limit of x divided by x as x approaches zero?  In this case, the answer is always 1 unless x is equal to zero, where it is undefined. The limit, therefore, is 1 , not infinity.\n\nA very important example.  If I am travelling 60 miles per hour, what is the limit, as the time  approaches zero, of (distance travelled in miles) divided (the time travelled in hours).  The limit is 60.  This kind of problem is the essence of differential calculus, which is important in just about every science, engineering and even social science field.
624175
When you divide by (m-n) since m=n you are dividing by zero, which is not right!
1098401
Check the problem again.  It doesn't simplify much ... I would have expected the terms with e^-x to either both be subtracted or added to one, not having the diferent signs you show.\n\nIt's not zero even how you have it written.  If x=0, the result is (1+1)(1+1)- (1+1)(1-1)/(1+1)^2.  Or 4 - 0 = 4.  The answer isn't 4 either (for all x).
1008854
Dont be fooled by the guy that might answer "Infinity plus one."  You know the problem with that.  How about "Infinity times infinity."
845874
1.  This is equal to\nk*(lnx)/x, and since \n(lnx)/x --> 0, so does this expression.\n\n2. Sorry, blank on this and 3.\n\n4. (n^k)/2n = (n^(k-1))/2, and I guess as long as \nk > or = 1\nthis will approach 0.\n\nOf course, if k < 1 then it has no limit, or "approaches infinity"