I know that divison by zero is undefined, but if you were foolish enough to do it what would it be?

Question

1/0=?
0/0=?
what would infinity divided by zero be or for that matter zero divided by infinity

computers can't do it, it needs thought, a pencil and paper help

anything divided by itself is one

I Know it is undefined!

and 1*1=1so what,that 0*0=0 is not a good answer,I know that part

many great mathematicians gave up on this, resulting in the undefined status,it is not a trivial puzzle

once again I understand Undefined very well, Why it is undefined I understand very well, I understand the work of Cantor on set theory and on Infinity an about aleph null
Why is it undefined and what are the possible interpretations

this is a start now, thanx

nice, tom a very plain proof of an impossible result

Answer 1

you get error from a computer, although some programs (like Matlab) can return you infinity as the result of 1/0.

0/0 is not defined and will cause an error in any computer program.

Answer 2

The root problem is that you cannot divide a number by zero. In calculus, one learns the concept of a limit, or what happens as I get mathematically close to a number, in this case zero. Consider dividing 1 by 1. The answer is 1, the identity. If I divide 1 by .5, get 2. If I divide 1 by .25, I get 4...divide 1 by .125, I get 8.... In other words, the smaller I make the divisor, the larger my answer gets. This is what is occuring when I take a limit. If I make the divisor infinitely small(ie keep adding zeros forever to the following number .00000000000000000000000000001), I will get an infinitely large answer. Infinity divided by zero would simply approach infinity faster than 1/0. 0/infinity is zero.

Answer 3

I think you're missing the meaning of "undefined." Undefined means, simply, that division by zero has no meaning. There is no definition for it. 1/0 does not mean anything. It has no mathematical concept.

Now, we can "approach" 1/0 and you'll get an idea. How much is 1/1? Now start shrinking the number on the bottom. How much is 1 divided by 1/2? By 1/4? By 1/100? By 1/1000000000? And so on.

As the number on the bottom gets smaller and smaller, 1 divided by that number gets larger and larger. However, when that number actually is zero, the division 1/0 has no definition.

Answer 4

Um... keep in mind that infinity is not a number, but a concept. Using it in an equation really yields no real results. And if a division by zero is undefined, how can you do it? Lol. Zero will never go into one. Zero always go into itself, but then again, you are dividing by zero which is undefined. We could create a number system to define these (or is there one? there might be..) Though it would be just about as useless as the imaginary system (actually , more useless, since you need that for complex numbers...). Gotta love messing with the unknown though!!

Answer 5

Division by zero is not undefined as much as it is not allowed. Following established rules of algebra, were division by zero allowed, it would be possible to prove, for example, that 2 = 1:

take any two numbers, X = Y

therefore X * X = X * Y

or X^2 = X * Y

therefore X^2 - Y^2 = X * Y - Y^2

therefore (X + Y) * (X - Y) = Y * (X - Y)

but therefore (X + Y) = Y and since X = Y then

therefore 2Y = Y or 2 = 1!

The flawed step is the penultimate division of both sides by (X - Y) which is of course division by zero.


As for infinity, there are actually different strengths of infinity. It can be shown for example that there are more real numbers than there are integers, although both are infinite.

Answer 6

Interesting way to look at 0/0 :) -

We know that any number multiplied by 0 = 0
For example, 3x0=0

Let forget the 0 for a moment. If we multiply 3 by 2, we get a 6 back. To undo this operation, we divide the 6 by 2.

In other words (3x2)/2=3

Now look at zero again. We have already noted that 3x0=0, so substitue this into the operation 0/0. We now have (3x0)/0. Based on our other example, we know that multiplying by 0, then subsequently dividing by it, should undo the first operation.

Therefore, (3x0)/0=3. Substitue 0 back in the place of (3x0), showing you that 0/0=3. Just as 0/0=3, 0/0 can also equal 4, or 5, or just about whatever you want it too :) .

Answer 7

1/0: is undefined
0/0: is nothing, this is called the indeterminate form, where no answers exists.
some rules of infinity:
1. infinity plus or minus any number n = infinity
2. infinity times infinity = infinity
3. infinity to a power of any number n = infinity
4. any number n divided by infinity = infinity
Special Cases:
5. infinity minus infinity = undefined
6. infinity divided by infinity = undefined
7. infinity times zero = undefined

Answer 8

it is not impossible to divide a number,depending on how you
define zero...for example if you divide something by the exact or complete zero like "[0]" (bracket zero) the answer Will be undefinable but if you divide thing by inexact zero like "0+" or "0-"
the answer will be infinity and it is definable like one infinity divided by another may result a real number (or even two inexact zero dividing each other),however an infinity divided by zero is infinity
and a zero divided by infinity is zero

Answer 9

What does the color green sound like? Asking what it would be like to divide by zero dosn't have any meaning. In a roundabout, purely academic way that is not useful in any analysis by any stretch of the mind, anything divided by zero is infinite, but since infinity is a concept and not a number, dividing by zero is not a mathematically defined operation.

As to your second series of questions, you can't divide by something that is not a number. Dividing by infinity is like dividing by "virtue". It is simply not going to work.

Answer 10

Okay I will try it
1/0 is Infinity
0/0 = 1 (because anything divided bt itself is one)
infinity / 0 = (1/0)/0 = 1 / (0x0) = 1/0 = infinity
0 / infinity = 0/(1/0) = (0x0) / 1 = 0/1 = 0