Does zero divide only zero?

Question

If it is true that zero divides only zero, then is it still possible to say that 0/0 is indeterminant? Please help.

Answer 1

Sorry to say, but all the answers above are wrong.



In INTEGER division, it's true that 0 divides only 0. This is a consequence of the definition of a|b (a divides b), where a,b ∈ Z:



a|b ⇔ ∃k∈Z (b = k×a)



Now, if a = 0 then, necessarily, b = 0 too, so:



0|a ⇒ b = 0



Now, this is different from the statement "0/0 is an indetermination" because, in this context, 0/0 doesn't refer to integer division, but to Real Analysis instead, and means that, if you have two real functions f(x) and g(x), such that:



lim[x → a]f(x) = lim[x → a]g(x) = 0



then lim[x → a](f(x) / g(x)) cannot be determined directly, and depends on the local behaviour of the particular functions.

Answer 2

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. 12 divided by 6 is 2 because 6 times 2 is 12 12 divided by 0 is x would mean that 0 times x = 12 But no value would work for x because 0 times any number is 0. So division by zero doesn't work.

Answer 3

no, it is not possible to divide by zero



zero=nothing; how could you divide by nothing ? is it possible ?



for example:



zero divided by number(0/x)



let a=0;

multiply by 1 on both side

a*1=0*1;

hence

a*1=0;

now take that one to other side

a=0/1;

that is nothing but

a=0;

so, any number which divides zero is zero



but if we take another statement(number divided by zero) x/0?

let a=0;

multiply by zero on both side;

a*0=0*0;

we may thing we can cancel the zero on both side but (once the values on the both sides are zero, we cannot put equal inbetween two conditions )

so, a*0=0*0===>0

hence, we cant divide any number by zero, if it is the condition, how come we can divide zero by zero??

Answer 4

No zero does not divide any number



even zero/zero(0/0) is an undefined number.



and if v divide any number by zero(0) then d solution will b infinite.



plz vote me the best answer.

Answer 5

zero does not divide zero. in fact it does not divie anything. everything divides zero.



x^2 / x tends to 0 as x tends to 0, but x / x^2 tends to infinity as x tends to 0. yet these two expressions come out as 0/0.



and it is possible to construct examples which tend to any limit you like. which is why it is indeterminant

Answer 6

Any number can be divided into 0.



You just can not divide any number by 0, including 0.

Answer 7

1. A number cannot be divided by zero, so it's not true that zero can only be divided by zero.



2. A number divided by itself equals 1, so 0/0 = 1 is false.



So, zero cannot be divided by zero.

Answer 8

Yes, zero divides only zero.

When 0 is divided by 0, remainder is 0 (whatever may be the quotient).But we cannot decide the quotient.0/0 is indeterminate.

Answer 9

Zero cannot divide any number including zero itself. Any number divided by same number the answer is 1. But this doesnot hold true in case of zero.

Answer 10

Yes and no. 0 does not divide 0, still undefined.

0/0 is indeterminate and you may apply L'Hopital's Rule.

Answer 11

If not in a purely math sense, I'd say 0/0 = 0.

That's because, when nothing is divided by nothing, it results in nothing.

Answer 12

Zero does NOT divide anything. In every case, the answer is indeterminate. ALWAYS.



Example from Calculus:



(X-3)/(X^2 -9) = ?

Plug in x=3 and you get 0/0 or 1 But is that correct? Try it again with x = 2.99

(2.99 -3)/(8.94 -9) = 0.01/0.06 = 0.1666666



(x-4)/(x^2 - 16) = ?

Plug in x=4 and you get 0/0 or 1 But is that correct? Try it again with x = 3.99

0.01/(15.92 - 16) =

0.01/0.08 = 0.125



Different answers as we get close to x. Very important result.

Answer 13

I think so because 0 is nothing.



It is an empty number



And also when you try dividing 0 by any nonzero digit in a scientific calculator, it reads out "Math error"

Answer 14

0/0

= undefined

Answer 15

0/0

= undefined

Answer 16

0/0=0

Answer 17

yes it is right zero divied only zero say it 0\0.

Answer 18

dont think so

Answer 19

No, it is undefined.

Answer 20

I don't know.