Joshua B.

asked • 07/30/16

If I divide a group containing 3 things by 3, I get 3 groups containing 1 thing each. Why then is it not possible that dividing that same group by 0...

...yield the result 1,1,1. Having divided 3 into no (0) groups (Not even the one it began with). 

Mark M.

How many times can you not do something?
That is why division by zero is undefined.
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07/30/16

Joshua B.

Just three, unrelated numbers. Not grouped by any construct.
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07/30/16

Joshua B.

But you are doing something - dividing. You're just dividing 3 things in one mentally constructed group, into 3 groups of 1 thing each. Why isn't it possible to take that same group and divide it into 3 unrelated units? In a sense, removing thier grouping. 1,1,1.
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07/30/16

Joshua B.

I undrstand why, conventionally, dividing by zero yields an undefined result. Especially when you view division as the inverse of multiplication. But by these terms, I'd like to know why it is wrong, or impossible.
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07/30/16

Joshua B.

Thanks for the reply by the way.
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07/30/16

Arturo O.

Dividing by zero simply leads to nonsense results.  For example, consider
 
1 x 0 = 2 x 0
 
The above equation is correct.  Now divide by zero on both sides, which cancels the zeros on both sides, and you get
 
1 = 2.
 
I hope this simple example makes it clear that dividing by zero leads to nonsense results.
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07/30/16

Joshua B.

By this concept: 1 ÷ 0 = 1
                              2 ÷ 0 = 1,1.
 
(Two things in 0 groups)
 
It seperate the link between division, and multiplication. Multiplication being unaffected by the change.
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07/30/16

Joshua B.

In multiplication zero determines how many times you perform the action. In division it determines, after having divided something, how many groups it ends up in.
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07/30/16

Joshua B.

I feel like 0 is functionally different in division.
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07/30/16

Joshua B.

Just want to know why that couldn't work. I'm not sold that it does.
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07/30/16

Joshua B.

It would mean 1 = (1,1)... so a rule would be needed for the number 1. Neat.
 
Dividing the 0 on both sides would now yield a different result. Though 1 is an odd example. As you still end up with 1, though you shed whatever thought group it was in.
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07/30/16

Joshua B.

So, a group of three oranges, divided by three, equals three new groups containing one orange each. Three oranges divided by zero, equals an orange, an orange, and an orange. Not in any mental grouping.
 
More clearly, six oranges divided by three, equals "three groups, containing two oranges each."
 
By zero, "an orange, an orange, an orange, an orange, an orange, and an orange." Same quantity, divided into no groups.
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07/30/16

2 Answers By Expert Tutors

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Kenneth S. answered • 07/30/16

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I think that your confusion emanates from over-application of the word DIVIDE.
 
Forget about 3 groups of 3 things--division of x by y is defined for any real number x and any real number y≠0.
 
Whatever you do to two groups of 3, you're separating or moving some of the contents of a set in order to make other sets.  This is not DIVISION.
 
Trying dividing on a calculator, with any choice of x and y EXCEPT choosing x=0.  These divisions work, and you get an answer.  But if you choose to divide BY ZERO, your calculator will not produce an answer--nor could you if you did long division on paper in this case.
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Joshua B.

Thanks for the reply. I'm challenging a fundamental idea that the calculator was programmed with, so granted - it wouldn't work. It would work on paper with this provision. The question assumes the provision.
 
3 ÷ 0 = 1,1,1. 
 
 
 
What is division if not an alteration of sets of items, or else the seperating of an item into sets/groups? I know the current rules. I'm looking more for why this couldn't work.
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07/30/16

Kenneth S.

Please release your grip on mis-applying the mathematical concept of division.
 
Then try refefining your problem WITHOUT using the word division.  Begin with certain sets, and describe your operation on those sets in precise English, without using the word division, because that would be using ÷ in a way that is out of context.
 
Have you studied any Boolean algebra (union, intersection, Venn diagrams, etc.)?
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07/30/16

Joshua B.

I have not. Ty for the council, I will do exactly that. 
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07/31/16

David W. answered • 07/31/16

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This reminds me of a friend's question about multiplying. To her, 3 x 0 = 3, because your not multiplying the 3 items and it stays as three items. In the same aspect, 3 x 1 = 6, because I took my 3 items and multiplied them once, so I now have 6 items.
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Joshua B.

Yeah,  I can see the mistake in that logic. Thinking you start with 3 items, instead of that you are multiplying the quantity of 0, 3 times. Nothing, nothing, nothing - still nothing. I just wish I had similar clarity for this idea.
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07/31/16

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