1divide by 0 is equal to what?

Answer 1

This problem is not computational. It does not involve calculators or limits or "just because." It is not a question about some "process" of division. Ask somebody to find 7/π by dividing up a set of 7 apples. That doesn't mean 1/π doesn't exist - it does.

This is firmly a question about the existence or nonexistance of the quantity:

1/0

1/x for any number x is the multiplicative inverse of that number. This is the definition of 1/x:

It is the UNIQUE number such that x × (1/x) = 1

However, for x=0, there is no such number. Why?

0 is the additive identity. y + 0 = y for any number y.

That means: 2×0 = 0 + 0 = 0.

Similar reasoning shows that y×0=0 for any y.

That means that there is no number "1/0" such that:

0 × (1/0) = 1

Thus 1/0 (the multiplicative inverse of 0) does not exist. Writing 1/0 has no mathematical meaning. It does not exist based ONLY on the definition of 0 and the definition of 1/x.

From this, you can extrapolate that k/0 does not exist for any number k, because if it did, you could write:

k/0 = k(1/0)

which still cannot exist.

Answer 2

1 / 0 = undefined

0 / 1 = 0

Consider why zero cannot be in the denominator...

Before we do so... think about what division means... the answer to a multiplication problem... (Do you agree that 15/3 = 5 if and only if 5 * 3 = 15?)

Let's say we can divide by zero, and let's call that answer A.
Let's do some 'algebra' stuff to it...

1 / 0 = A [multiply each side by 0]
0 * 1 / 0 = 0 * A [the 0 / 0 'cancels' to give 1]
1 * 1 = 0 * A
1 = 0 * A [what could A be here? Isn't anything * 0 = 0?]
1 = 0
That makes no sense!

Well... let's get clever here... I know 0 = 0.
So what about 0 / 0? That's got to be possible?

0 / 0 = A [multiply each side by 0]
0 * 0 / 0 = 0 * A [the 0 / 0 'cancels' to give 1]
1 * 0 = 0 * A
0 = 0 * A [what could A be? 12? Pi? -84?]
But here, everything makes sense for 0 / 0 having an answer.

So, instead of having nothing as an answer in the case of a number divided by 0 and everything as an answer in 0 divided by 0... mathematicians have decided neither ... UNDEFINED when you're talking about division by zero (a.k.a. zero in the denominator).

By the way, E in your calculators means error. It's your calculator's way of saying "you can't do this operation."

Others on here are discussing limits... limits are completely different from straight forward division. Be careful!

Answer 3

you cannot divide anything by 0, if you do, it is an undefined value...so the answer would be
Undefined

however, if you divide 0 by a number..it will be 0...

this is because 1 divided by 0 would be the same as saying:
1 can be put into how many groups of 0..which doesnt make sense at all..so it has to be undefined.

but 0 divided by 1 would be saying:
0 can go into how many groups of 1...that has to be 0 times becuase 0 can't go into any groups...

if you need more help, just tell me :]

Answer 4

It is undefined, as various people have already stated. By mathematical convention, division by zero is not a permitted operation because it leads to contradictions (an example of which has also been given in an earlier answer).

A lot of programming languages do return infinity for (anything) divide by zero but, strictly speaking, they are wrong. Some languages get it right by returning NAN (Not A Number).

Calculators give the answer as E because they are reporting it as an Error. So, in a sense, they are correctly classing it as a non-number (not infinity).

Also, the statement that 1/n tends to infinity as n tends to 0 is *nearly* correct. It is true when n>0. But when n tends to 0 and n<0, 1/n tends to negative infinity.
n = -1 1/n = -1
n = -0.01 1/n = -100
n = -0.0001 1/n = -10,000
etc.

Answer 5

Dear Herish...
The short answer
It's infinity (a symbol to point to a big than can be imagined)

Zero is equivalent to say a very small quantity or not exist
in this manner if we divide a thing into a verrrrrrrrrry small parts of it we will get mannnnnnnny parts,

Continue with this the answer should be self evidence

Answer 6

x/0 is equal to both nothing at all (not to confuse nothing with zero) or positive and negative infinity.
Therefore, because there are two completely different answers anything divided by zero is undefined.

Answer 7

1 / 0 = cannot be defined.

Try doing it in Excel. It won't give you any result. Instead it will return an Error prompt.

Answer 8

equals to nothing and here is proof:

imagine 1 / 0 = k (a number)

then muliply 0 by both sides

0 * ( 1 / 0 ) = 0 * k

====> 1 = 0 which is wrong

so 1 over 0 is undefined

Answer 9

The correct answer is undefined. At the limit as X approaches zero, (1/X) approaches infinity.

1/X
1/100 = 0.01
1/10 = 0.1
1/2 = 0.5
1/1 = 1
1/0.5 = 2
1/0.1 = 10
1/0.01 = 100
1/0.001 = 1000
1/0.0001 = 10000
1/0.00001 = 100000
1/0.00000000001 = 100000000000

So as X gets smaller and smaller the result of 1/X gets larger and larger. As there is no limit to the smaller and smaller X, there is no limit to the larger and larger result. It is infinite. But to directly divide anything by zero makes no sense.

Answer 10

Undefined.

Can't divided by zero