- #1

#### Ahmed Jubair

__0/0=1__.but Again,it couldn't be (-1) also i think because if its-5/5=5,-2/2=-2.but 0 have no value and its the low valuenumber.so no need a( - )before it.so(- 0/0 is not =-1)

then why its undefined?why not

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- Thread starter Ahmed Jubair
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then why its undefined?why not

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- #2

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Dividing by 0 is undefined.

You can't divide anything by 0 ... including 0!

You can't divide anything by 0 ... including 0!

- #3

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[tex] \frac{0}{0}=\lim_{x\to 0} \frac{x}{x} = 1[/tex]

But this is not the only possibility. Why couldn't I define:

[itex] \frac{0}{0}=\lim_{x\to 0} \frac{2x}{x} = 2[/itex] or : [itex] \frac{0}{0}=\lim_{x\to 0} \frac{x}{2x} = 1/2[/itex]

or in an infinite number of other ways? That is why it is undefined.

- #5

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I don't understand what you're doing here. -5/5 = -1, not 5, and -2/2 = -1, not 2Ahmed Jubair said:if( 2/2=1,5/5=1) then it must be that0/0=1.but Again,it couldn't be (-1) also i think because if its-5/5=5,-2/2=-2.

Certainly 0 has a value.Ahmed Jubair said:but 0 have no value

?Ahmed Jubair said:and its the low valuenumber

It's the smallest number that isn't negative.

Ahmed Jubair said:.so no need a( - )before it.so(- 0/0 is not =-1)

then why its undefined?why not1

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One could now object: But ##1## as the neutral element of multiplication is part of the additive group, it even generates it.

My answer then would be: ##1## has a natural usage for addition, ##0## hasn't for multiplication. The definition ##0 \cdot 1 = 0## simply is a necessity for the distributive law which is the only connection between both operations.

- #7

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That's a nice explanation. I really love how such a simple question can have such a variety of legitimate answers.fresh_42 said:

One could now object: But ##1## as the neutral element of multiplication is part of the additive group, it even generates it.

My answer then would be: ##1## has a natural usage for addition, ##0## hasn't for multiplication. The definition ##0 \cdot 1 = 0## simply is a necessity for the distributive law which is the only connection between both operations.

- #8

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So for example:

20 -5 -5 -5 -5 = 0

So the result of 20/5 = 4 (how many times did you repeat the 5?)

Now for the zero:

0 - 0 = 0 ... Well I reached zero (so 0/0 = 1)

How about this:

0 - 0 - 0 - 0 = 0 I reached zero too ( 0/0 = 3 )

So you can see that you can make infinite answers. So when you divide 0/0, you can't just choose one of the answers because Why not the others too?

That is how I see it which is similar to Blue_Leaf way

- #9

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Let a=b, if we multiply both sides by a..

a^2=ab ,now subtract b^2 from both sides.

a^2-b^2=ab-b^2

Now simply factorise:

(a-b)(a+b)=b(a-b) , now divide both sides by (a-b).

So we're left with, (a+b)=b

Using our original definition of a=b, we can simplfy this to 2b=b which implies that 2=1, which is mathematically incorrect. The mathematics of my steps were valid until the point where I divided both sides by (a-b), [a-b=0]. So as you can already tell, dividing anything by zero is not possible. Many other good reasons have been explained here. Try a graphical approach if you're really interested, and plot as many graphs as you can that pass through (0,0), the trend you will notice is that there are an infinite amount of ways to approach 0 and thus we cannot give it's division a value.

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It's also interesting to note that you can't divide any number by another and obtain a non-approximate zero.

Pure mathematics makes my head hurt.

- #11

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It is not. 0 has nothing to do with multiplication. There is no need for an inverse!Marcus-H said:It's an axiom that division by zero is undefined, ...

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fresh_42 said:It is not. 0 has nothing to do with multiplication. There is no need for an inverse!

Hmm I was using 'axiom' in it's broadest sense though your point is well taken, thanks.

- #13

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No, this isn't valid. Since a = b, by assumption, then a - b = 0, so you're dividing by zero.whit3r0se- said:One could also use a proof by contradiction here.

Let a=b, if we multiply both sides by a..

a^2=ab ,now subtract b^2 from both sides.

a^2-b^2=ab-b^2

Now simply factorise:

(a-b)(a+b)=b(a-b) , now divide both sides by (a-b).

If you do that, all bets are off, which you explain below.

whit3r0se- said:So we're left with, (a+b)=b

Using our original definition of a=b, we can simplfy this to 2b=b which implies that 2=1, which is mathematically incorrect. The mathematics of my steps were valid until the point where I divided both sides by (a-b), [a-b=0]. So as you can already tell, dividing anything by zero is not possible. Many other good reasons have been explained here. Try a graphical approach if you're really interested, and plot as many graphs as you can that pass through (0,0), the trend you will notice is that there are an infinite amount of ways to approach 0 and thus we cannot give it's division a value.

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"non-approximate zero"? What is that?Marcus-H said:It's an axiom that division by zero is undefined, conceptually it makes sense because it makes no sense to ask ' how much nothing goes into something '.

It's also interesting to note that you can't divide any number by another and obtain a non-approximate zero.

If you divide any nonzero number by itself, you get 1.

Marcus-H said:Pure mathematics makes my head hurt.

- #15

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Time to put this thread to bed. The question has been asked and answered. Division by zero is undefined, and that's all you need to say.

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