Division by zero?

Question

Why is that division by zero is impossible and undefined? Also, if zero is divided by zero, would the result remain to be undefined, or would the result be 1 or 0? If possible, I would like some sites with some proofs with 0/0 equaling 1 or 0.

Answer 1

Imagine a simple fraction:



1 / 1 = 1

1 / (1/2) = 2

1 / (1/10) = 10

1 / (1/2,000) = 2000

1 / (1/1,000,000) = 1,000,000



OK, so can you see that as the denominator gets closer to zero that the result of dividing by it is that your answer gets incredibly large? If you take it to the extreme and divide by zero you'd theoretically get an answer of infinity which is obviously ridiculous (in this sense of this equation).

Answer 2

It's impossible because 1) it makes no sense in practical terms and 2) it leads to impossibilities in mathematics.



Dividing by a number means "How many sets of this number can I make?" If you have 12 items and wanted to make piles of 4, you could make three piles, because 12 divided by 4 is 3. If you did that with 23 items you could make 5 piles and have 3 items left over, which is why 15 divided by 4 is 5 with a remainder of 3. If you had 0 items, well you could make exactly 0 piles. But dividing a number BY zero means "Keep making piles of 0 until you run out of items." If you have 5 items and try making a "pile of zero", you still have 5 items left, so matter how many "piles" you make.



Let's say 5/0 was some value x. Then 5/0 = x. But multiplying both sides by 0 gives 5 = 0*x. There is no number which when multiplied by 0, gives you back 5.



0/0 is not "undefined" but a special case called "indetermined". This is because 0/0 can in fact have ANY value you want. If 0/0 = x, then 0 = 0*x. Again, x can be anything.

Answer 3

We cannot take 4 apples and divide them into "zero" groups.



4/0 means we have 4 'parts'.

The denominator means that the 'whole' is divided into zero groups. Zero groups? They are just not there, no groups! So how can we have four parts of them?



Also

x*0=0 and is true for any value of x. So we cannot invert the multiplication with division. Because how can you have a division problem where division & multiplication yield the same answer?



Division by zero is allowed in a certain instance (Reimann Sphere), but it does not disprove that any number ÷ 0 is undefined.

Answer 4

0/0 is considered to be an undetermined form in calculus. In calculus you evaluate a limit via l'hopital's rule if the original limit equals an undetermined form such as 0/0.. there's a reason for that, but I do not know the proof off of the top of my head.



Think about it this way... Something big divided by something small is the samething as something big. For example....

5/1 = 5, 5/(1/2) = 10, 5/(1/10000) = 50000.. 1/0 is undefined or "defined as infinity" so to speak.

Answer 5

try to imagine cutting a pie into pieces a nothingness of an inch wide



how many pieces do you think you would get? and how would you put them back together again?



also if division by zero was possible, you could prove any number was equal to another one



eg



2 x 0 = 1 x 0



dividing both sides by 0 gets



2 = 1



if you draw the graph y = 1/x, as x approaches zero, y seems to approach infinity

Answer 6

Division by 0 yields no result at all. If you divide a number by 0 you will always receive an error prompt. In other words, there is no solution on a number divided by 0.

Answer 7

division by 0 is undefined since you can't, by convention, split x things into zero groups. [even if x is zero!]



however, the LIMIT as x approaches zero for a function like 1/x, equals infinity.

Answer 8

Dividing 0 by 0 is like taking nothing and dividing it between 0 people. How much sense does that make?

Answer 9

its impossible to divine nothing with nothing

if you say that 0/0 = 0 than 10/0 = 10, that how about 10/1?

It only make a complicated in math

Answer 10

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Answer 11

You can go to the following url for answers.



http://mathforum.org/dr.math/faq/faq.divideby0.html