Dividing by Zero?

Nothing divided by nothing is still nothing even if it were a a valid mathematical operation (which it isn't).

Additionally it (0/0) has absolutely no mathematical use, so the question is rather redundant. Why do you ask?

Thank you for your response which states "nothing/nothing =Nothing so therefore 0/0 =0 not 0/0=1 it seems we are in disagreement. If this is not a valid mathematical operation Why did you perform it? best regards, K

Since my simplistic answer with its basic example wasn't good enough why don't you have a closer look at the math behind the math of division by zero.

http://en.wikipedia.org/wiki/Division_by_zero

Plenty more detailed answers and theorems on the web.

In regard to your original question

can one successfully divide by zero ?

The answer depends on your definition of 'successfully' as the answer is known but indeterminate (hence rather impractical except from a theoretical point of view).

Again, why do you ask (I am assuming it is a theoretical question)?

Thank you for your response My position is that 0/0 =1 is the "best answer" since in all other cases that i am familiar with (and my familiarity is quite limited) x/x=1, i/i=1 , e/e=1 ad infinitum

0/0 could be x, though, or 2, or 588839520043 or "#DIV0!", as Excel might say.

The fact that it could be anything makes the operation itself invalid; there is no singular answer to the question in the language of mathematics.

Kay & OP,

In strict terms 0/0 is an undefined action by itself. As others (PWSlack?) have posted here. By undefined it means that it could be anything. So saying 0/0 =1 is the "best answer" is wrong for you omit all of the other possible answers. But if how you reached this undefined division is defined then a value can be defined. Lets take the example you cite. You define the numerator as f(x)=x and the denominator as g(x)=x so in this calculation of f(0)/g(0)=0/0=1. But one does not have to reach this division by only this pair of simple functions. If f(x)=2x and g(x)=x then f(0)/g(0)=0/0=2. Also if f(x)=x³ and g(x)=x then f(0)/g(0)=0. If f(x)=sin(x) and g(x)=x then f(0)/g(0)=0/0=1. This last relationship is a very important relationship one finds in wave mechanics. How to ascertain which value this division generates for each family of functions is spelled out clearly and precisely in applying l'Hopital's rule.

Actually, you might want to look at Seyfurt's third theorem which clearly shows that 0/0 = 1 only in the limit in which 0 approaches 7. A lot of mathematicians reject this as a blatant example of dialectic maternalism, but choose for yourself.

Cheers

tell me more of seyfurts third theorem it seems to support my argument. Since identity theorem states"All values multiplied by 1 = said value therefore all values/said value =1

You are correct in that 0/0 = 1 ......... also:

• 0/0 = 2
• 0/0 = 3
• 0/0 = 0
• 0/0 = 3.14
  
• 0/0 = anything because it is indeterminate

ANY number qualifies as zero divided by zero. It is when you get to dividing
NON-zero numbers by zero that you confront infinities.

Think of this in terms of the definition of division. A divided by B
means: How many times must you subtract B from A to reach zero?

For A divided by zero, where A is any number except zero, the number is
not even infinity, because infinity itself is not big enough. No matter
how many times you subtract zero from, say, five, you will never, ever
reach zero. So even infinity is not big enough to be 5/0.

What does this tell us about zero divided by zero? Well, how many times
must you subtract zero from zero in order to reach zero?

Zero times? Sure. That works.
One time? That works too.
Two times? Yes. If you subtract zero from zero twice, the result is
zero.
Pi times? Again, if you subtract pi zeroes from zero, the result is
zero.

We can do this with ANY NUMBER THERE IS, even zero. So, zero divided by
zero is truly a special way to define a number. The answer can be
infinity, or it can be zero, or absolutely anything else. All numbers
satisfy the operation.

Thank you for your thorough response, it is nearly identical to the one my father(a brilliant mathemetician)gave me 45 yrs. ago. in pure numbers you have me but how does this apply in finance lets say for instance our income statement says we made 0 $ in the third quarter of 2008 our income statement also says we lost 2 million $ in the second quarter . 0 now represents a value If we let i represent the sq. root of -1 What is i/i is it 1? best regards K

You lost me with the finance part.

It seems you are asking two different questions.

But, yes i/i = 1

(even the omnipotent Google agress: http://www.google.com/search?q=i%2Fi&btnG=Search)

so your position is we can divide an imaginary number "i" by itself(i) and arrive @ 1 yet we can not divide areal number by itself and arrive @ 1 ....interesting!!!

who said we can't divide a real number by itself and arrive @ 1?

I know I said 0/0 MAY equal 1, or 2, or ......

I like your style,prove me wrong 0/0=1

SEE MY ANSWER / REPLY #17.

You are right and you are wrong

I say that 0/0 equals 4,239.716

and I say you do not have the "best" answer because you have no other occurences to prove it. My proof is x/x =1 and it occurs ad infinitum where is your support for 4,239.716 Let me offer another non math/non science question since you strike me as more than "reasonably astute". The universe contains an infinite number of stars.The universe contains An infinite number of galaxys . how is this plausible since stars make up galaxys

Uhh-ohhh!!! not the "infinity" issue!!!

I will start with the 0/0 issue, with the simple basic:

Let us take the definition of "division" as the inverse of "multiplication"

Webster's Online Dictionary:

Divison: noun

An arithmetic operation that is the inverse of multiplication; the quotient of two numbers is computed.

Therefore, I submit that 0*4,239.716 = 0

"An infinite number of galaxys . how is this plausible since stars make up galaxys"

No, no, no. Everyone knows Galaxys are made of left-over Edsel parts.

You said

"

SEE MY ANSWER / REPLY #17.

You are right and you are wrong

I say that 0/0 equals 4,239.716"

NO! NO! Were you not paying attention in math class? Were you secretly checking out that cheerleader in the front row?

0 has one significant digit. Therefore, the answer can have only one significant digit. You must round off 4,239.716 to one significant digit. Personally, I like the digit "B", but suit yourself.

0 = 0 + 0

0/0 = 0/0 + 0/0

1 = 1+ 1

1=2

similarly 1=3, 1=4 and yes 1=0 from

0 = 0 - 0

"So, zero divided by zero is truly a special way to define a number ..."

No, it is not "a way to define a number" because division by zero is itself strictly undefined.

However, it is possible to consistently define division by zero in other mathematical systems, for instance on the Riemann sphere. In hyperreal and surreal number systems division by non-zero infinitesimals is possible, but these infinitesimals are not strictly zero so, in sense, we're fudging.

If a number system forms a commutative ring as do the Real and Complex numbers, the ring can be extended to a wheel in which division by zero is always possible, but in these systems the division operation itself takes on a somewhat different meaning.

-e

If i/i =1 and i is indeterminant how does one arrive at a determinant conclusion with indeterminant terms (such as "i") yet one is forced to arrive at an indeterminant conclusion with determinant terms i.e.0

'i' is indeterminate so in every case where 'i' is >=1 or 'i' <=1 (ie 'i' is anything but not 0) then i/i will always be equal to 1 (eg- 6/6=1, -2/-2=1, etc).

I was letting "i" represent the sq. root of -1 ,not any integer, (sorry)

Q: What does the ratio i/i (where i = [-1]^½ ) have to do with division by zero?

A: Nothing.

i is not indeterminate, it is imaginary, or the latter half of a complex number.

Where it is exactly defined as i² = -1

It all depends on how one reaches 0/0. The most common way to solve this is the application of l'Hopital's rule. This is a simple rule, covered in Calculus, but does require understanding how to take the limit of a function. (Specifically the limit as one approaches the result of 0 for both the numerator and the denominator simultaneously.) So it may not be covered in Calculus 1, but quickly by Calculus 2 for an understanding of many operations hinge on knowing this important rule.

This rule also permits finding the result of ∞/∞, most of the time.

all i know of calculus is that Liebnitz postulated that 1.999... is equal to 2 since the difference of the pair was not ascertainable or measurable. i am merely suggesting that 0/0 =1 because its a logical conclusion. Thank you for your input and please reply

YES!!!

0/0 DOES EQUAL 1, as it also equals 2, 521.6041, 18, ......

Look at it this way:

11/2 = 5.5

For example, if you have 11 carrots you may take away a pair (2), 5 and 1/2 times until you have zero carrots remaining in the original lot.

Now, imagine you have zero carrots, you may then take away 1 zero and be left with zero carrots in the original lot. You may also take away 15 zeros and still be left with zero carrots in the original lot. Or you may take away 0 zeros and still be ..............

We had a very stimulating discussion " bucking" the basic laws of mathmatics . Thank you all for your well thought out responses! My next question will be far less simple to refute! Best wishes to you all K

Ah yes, but what exactly is zero? Has it really been defined as nothing, can one actually have nothing? Absolute Zero anyone?

so 1 x bowl of dogs vomit divided by itself = a mess?

Precisely!!!!!!!

0/0 can not be determined.

0 by some number is zero.

some number by 0 is infinity.

So 0/0 is under push-pull, somehwere between 0 and infinity we do not know.