Math Is Fun Forum

chatalot

Real Member

Registered: 2006-12-23

Posts: 125

Imposible Question

My 3rd grade brother was given a home-work assinment or pages of maths questions. He asked me to correct it, so I did. But one of the question was imposible. Can any of you make sense of this?

0 devide by 0 is:

I asked my mother (a fully qualified maths teacher) and she could not make sense of it to. So can any of you make it possible?

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John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Imposible Question

Anything divided by itself is ONE.  So I would say ONE is the answer.
However, most will agree the problem is UNDEFINED, which means it has no answer.

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Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Imposible Question

The answer from analysis would be undefined.  From algebra, I would say the answer is that the question doesn't make sense.

a/b means "a times the multiplicative inverse of b".  The multiplicative inverse of b is a number b-¹ such that b * b-¹ = 1.  So we are looking for a number, call it c, such that 0 * c = 1.  Of course, 0 times anything is 0, and so such an inverse doesn't exist.  So you are asking to multiply by something that doesn't exist, and thus, the question doesn't make sense.

But most people stick to analysis and just say "undefined".  Why?  I think it's because "undefined" is at least some sort of answer.

Anything divided by itself is ONE.  So I would say ONE is the answer.

This is certainly incorrect.  For assume that 0/0 = 1.  Then it must be that:

But we also know that:

So it must be that 0/0 = 2.

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chatalot

Real Member

Registered: 2006-12-23

Posts: 125

Re: Imposible Question

Anything divided by itself is ONE.  So I would say ONE is the answer.
However, most will agree the problem is UNDEFINED, which means it has no answer.

But  0*0=0, so shouldn't 0/0=0?

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Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Imposible Question

And 0*1 = 0, and 0*2 = 0.  So if you were to "divide by 0" (my original post shows that this doesn't even make sense), then all of these equations hold.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Imposible Question

Anything divided by itself is ONE.  So I would say ONE is the answer.

No. Not anything. If that were the case, I could also claim that ZERO divided by anything is ZERO and say that was the answer instead.

0∕0 is undefined. End of story.

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: Imposible Question

"Indeterminate"

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Identity

Member

Registered: 2007-04-18

Posts: 934

Re: Imposible Question

I would say 'indeterminate' is a little more accurate than 'undefined'. Undefined means 1/0 or 2/0, where the answer is just that, but indeterminate means there is more than one answer.

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Imposible Question

I agree with 'indeterminate'.
However, this discussion is on a far more advanced subject than a 3rd-grader should be thinking about.

I suspect that his teacher decided to be slightly evil and set a question designed not to be answered, but just to be pondered.

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Stanley_Marsh

Member

Registered: 2006-12-13

Posts: 345

Re: Imposible Question

0/0 seems invalid to me . 0 can't be the denumerator .that's the rule.

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chatalot

Real Member

Registered: 2006-12-23

Posts: 125

Re: Imposible Question

Well his teacher apologised. She had just made a mistake.

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