The Way I See It, You Can Divide A Number By 0 And Get A Whole Number Answer

[ZacharyNardolillo]

Well to start off let me say what division is. I'm quite sure it literally means: to take X and spread it out among Y groups. Even though it can is often said as "how many times X goes into Y", im quite sure that is technically incorrect.

 

Since multiplication and division are opposites, you could say they have opposite meanings. multiplication means to take and X and make it into a group where there are Y X's, not realy X goes into Z Y times. So why would wouldn't you apply this method backwards with division?

 

Using the first method (of division), 15/0 = 0, because 15 spread out equally among no groups would yield nothing. Using the second method, the equation would read 15/0 = infinity. So why is it regarded as impossible, when 15 spread out equally accross 0 groups clearly equals 0?

 

Another supporting piece of evidence: addition and subtraction. When you add or take away 0 from X, you end up with the same answer. So looking at addition and subtraction as an example, wouldn't division and mulitiplication have a similar reaction?

[steve 9]

Funny, I was just talking about this with someone yesterday. My questions were a bit different. I will use your examples to point out something that I found interesting.

 

 

 

Well to start off let me say what division is. I'm quite sure it literally means: to take X and spread it out among Y groups. Even though it can is often said as "how many times X goes into Y", im quite sure that is technically incorrect.

 

Since multiplication and division are opposites, you could say they have opposite meanings. multiplication means to take and X and make it into a group where there are Y X's, not realy X goes into Z Y times. So why would wouldn't you apply this method backwards with division?

 

Using the first method (of division), 15/0 = 0, because 15 spread out equally among no groups would yield nothing.

 

In this first example you are saying that 15 spread out equally among no groups would yield nothing. Well in order to make this a real world equation we will have to say 15 what? Lets say we have 15 apples, now if we try to spread them out among no groups, or we have no other places to put them equally, or we just can not put them anywhere, we are stuck with the 15 apples. If we have 15 apples and do nothing with them then we will have 15 apples. Right?

 

So it would look as though 15 apples not divided equals 15 apples. 15/0 = 15

 

 

 

Using the second method, the equation would read 15/0 = infinity. So why is it regarded as impossible, when 15 spread out equally accross 0 groups clearly equals 0?

 

I am not sure what you mean here, but again, 15 what? If you have 15 of something and do nothing with it you will still have 15 of the something.

 

Just a thought.

[Gordon Freeman]

I don't think he initially wanted a real life example, but I'll try to solve it as a pure mathematics question first, and then give a real-life example.

 

The reason the idea of no solution being the solution to the divinity of zero, was because of a plotted chart example of 1 divided by every number. No matter what you divide one by, it will never equal zero (excluding the division of zero as something to divide one into), and no matter what you multiply with one (again, excluding zero) it will never equal zero. If you graph this, you will see how the line comes closer and closer to the origin on the graph, but slowly turns away from it, bolth ends showing exponential properties. I probably butchered the full explanation, but I think you get the point.

 

Not to mention, if the division of zero was a practical mathematical affect, many standard equating systems would be null, as the use of zeros would radically change.

 

In a real life example, if it is still necessary, there is no such thing as placing a whole into imaginary groups (that is to say we're not dealing with number theory, but just the practical application). So the division of zero in real life is irrelevant because it's the same as an imaginary friend, which most people you know have probably named 'God', you get the point? You could do it, in theory, but you would never be able to physically do it in real life. So the use of it's division becomes null.

 

If any of you find the theories on it's pure math. use, link the thread here, so the OP can see that it is potentially possible, but with no real application outside of physics (at least that's what is seems to be most relevant to).

 

I hope that cleared it up.

[Boerseun]

A pretty simple way of looking at it, is to imagine making piles of stuff - if you want to divide ten by two, you get to make two piles and split the number you're dividing equally into the two piles, leaving you with two piles of five each, which will be your answer. The amount of equally divided stuff in a single pile will be the answer to your original question, 10/2. So, 10 (original number) / (divided by) 2 (the number of piles) = 5 (the number of stuff in a single pile after you've divided it).

 

When you want to divide by zero, it looks like this 10/0 = CAN'T BE DONE. Look closer:

 

10 (original number) / (divided by) 0 (the number of piles) = CAN'T BE DONE (the number of stuff in a single pile after you've divided it - which is now impossible, because there are no piles to count the content of.)

 

Sorry if this explanation comes over a bit juvenile-like, but it kinda gets the point across.

[Tormod]

I like the wikipedia article on division by zero:

 

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

[ZacharyNardolillo]

Funny, I was just talking about this with someone yesterday. My questions were a bit different. I will use your examples to point out something that I found interesting.

 

 

 

 

 

In this first example you are saying that 15 spread out equally among no groups would yield nothing. Well in order to make this a real world equation we will have to say 15 what? Lets say we have 15 apples, now if we try to spread them out among no groups, or we have no other places to put them equally, or we just can not put them anywhere, we are stuck with the 15 apples. If we have 15 apples and do nothing with them then we will have 15 apples. Right?

 

So it would look as though 15 apples not divided equals 15 apples. 15/0 = 15

 

 

 

 

 

I am not sure what you mean here, but again, 15 what? If you have 15 of something and do nothing with it you will still have 15 of the something.

 

Just a thought.

 

 

I see what you're saying here, but I wasn't using 15 as a group of physical objects, just a theoretical and generic number. Also, 15/0 = 15, It seems, would be basically what divided by 1 is: you just leave everything in the same group.

 

Another thing worth noting is dividing by fractions, which actually multiplies the number, so I guess you could say that /0 would equal infinity since there would be an infinite number in a space so small, but one thing to remember is this: It's not a small space, it's just nothing. lol sorry that had nothing whatsoever to do with your post, but It seemed worth noting.

[granpa]

whats the sound of 4 hands clapping?

whats the sound of 3 hands clapping?

whats the sound of 2 hands clapping?

whats the sound of 1 hand clapping?

 

just because 1/x is defined for all other x doesnt mean that it is defined for x=0

 

whats north of the north pole? The question has no meaning at the north and south poles even though it is well defined everywhere else.

 

It is 'unknowable'. (Or 'paradoxical' if you prefer)

[modest]

Well-said, Grandpa

 

Well to start off let me say what division is. I'm quite sure it literally means: to take X and spread it out among Y groups.

 

I think your definition is missing an essential part. Division involves not only the dividend, X, and the divisor, Y, but a quotient, Z, where X/Y=Z. Division gives the quotient—the size of the group in this case. I think your definition should be more like "to take X and spread it out among Y groups of size Z".

 

I believe your method is sometimes called 'division by partitioning'. An equally-admissible method is quotative division which is to say "X is spread out into groups of equal size Y making Z groups". In the former the number of groups is the divisor and in the latter the size of the groups is the divisor.

 

As an example, division by partition would say that 12 gallons of milk divided by four containers makes 3 gallons each. Quotative division would say that 12 gallons of milk divided into 3 gallon containers makes 4 containers.

 

To divide by zero is to ask either, "How large are the containers that divide one gallon of milk evenly into zero containers?" or,

"How many containers of zero volume will one gallon of milk fill?"

 

You can see that infinity makes a little more sense than zero, but the questions are in a sense paradoxical.

 

~modest

[IDMclean]

Well-said, Grandpa

 

 

 

I think your definition is missing an essential part. Division involves not only the dividend, X, and the divisor, Y, but a quotient, Z, where X/Y=Z. Division gives the quotient—the size of the group in this case. I think your definition should be more like "to take X and spread it out among Y groups of size Z".

 

I believe your method is sometimes called 'division by partitioning'. An equally-admissible method is quotative division which is to say "X is spread out into groups of equal size Y making Z groups". In the former the number of groups is the divisor and in the latter the size of the groups is the divisor.

 

As an example, division by partition would say that 12 gallons of milk divided by four containers makes 3 gallons each. Quotative division would say that 12 gallons of milk divided into 3 gallon containers makes 4 containers.

 

To divide by zero is to ask either, "How large are the containers that divide one gallon of milk evenly into zero containers?" or,

"How many containers of zero volume will one gallon of milk fill?"

 

You can see that infinity makes a little more sense than zero, but the questions are in a sense paradoxical.

 

~modest

Seems similar to the Banach-Tarski Paradox.

[questions]

10 x 2 = 20

20/2 = 10

 

10 x 0 = 0

0/0 = 10?

 

I know what you are saying but dividing by 0 does not make sense.

 

I have 6 cookies. I place them into 2 groups. I have 3 cookies in each group.

6-2=4 - Created the first group.

4-2=2 - Created the second group.

2-2=0 - Created the last group. No cookies left so I can create no more full or partial groups.

6/2=3

 

I have 6 cookies. I place them into 0 groups. How many cookies do I have in each group?

6-0=6 Created the first group out of nothing.

6-0=6 Created the second group out of nothing.

6-0=6 Created the third group out of nothing.

...

 

So wait, does that mean it is infinite? 6/0=(infinite)

If so that means (infinite) times 0 is 6. Or any number for that matter.

 

See? Dividing by 0 does not make sense.

 

Dividing by 0 is NOT 0. It is not true that you create no groups. But rather you COULD NOT make any groups. Dividing by 0 does not equal the number as someone said. Your logic was putting it into one group. The answer to a divide by 0 problem is undefined, because you CANNOT do it.

 

Hope this helps.

[Qfwfq]

You have 12 eggs in the fridge and your dietician recomended 3 eggs every day. How many days will that supply last? After each day there will be 3 less in the fridge, after the fourth day there will be no more. Suppose instead your dietician directed you to eat no eggs, how many days will the same supply last? They will never run out.

[ZacharyNardolillo]

10 x 2 = 20

20/2 = 10

 

10 x 0 = 0

0/0 = 10?

 

I know what you are saying but dividing by 0 does not make sense.

 

I have 6 cookies. I place them into 2 groups. I have 3 cookies in each group.

6-2=4 - Created the first group.

4-2=2 - Created the second group.

2-2=0 - Created the last group. No cookies left so I can create no more full or partial groups.

6/2=3

 

I have 6 cookies. I place them into 0 groups. How many cookies do I have in each group?

6-0=6 Created the first group out of nothing.

6-0=6 Created the second group out of nothing.

6-0=6 Created the third group out of nothing.

...

 

So wait, does that mean it is infinite? 6/0=(infinite)

If so that means (infinite) times 0 is 6. Or any number for that matter.

 

See? Dividing by 0 does not make sense.

 

Dividing by 0 is NOT 0. It is not true that you create no groups. But rather you COULD NOT make any groups. Dividing by 0 does not equal the number as someone said. Your logic was putting it into one group. The answer to a divide by 0 problem is undefined, because you CANNOT do it.

 

Hope this helps.

 

 

I see what you're saying here, doing multiplication backwards to get division, but remember: There are many exceptions to rules in math. for example, It is safe to say any even number is not prime. except for 2, the one and only exception to the rule. See what I mean? Also, you said that you put zero cookies in the first group, but at that point you had allready gone too far. you weren't supposed to make one, two, three, or more groups, just 0.

[Donk]

As has been said above, division is the inverse of multiplication. But remember that multiplication can be treated as repeated addition:

 

(4*3 = 4 + 4 + 4)

 

And division can be treated as repeated subtraction:

 

12/4 = 12 - 4 - 4 - 4

 

Looking at it this way, it's quite clear that you can subtract zero as many times as you like, all the way up to infinity, without changing the original number.

[modest]

I see what you're saying here, doing multiplication backwards to get division, but remember: There are many exceptions to rules in math. for example, It is safe to say any even number is not prime. except for 2, the one and only exception to the rule.

 

2 is not an exception to any rules about prime numbers. A prime is a natural number that has two natural number divisors (1 and itself). Nothing about that definition implies that a prime number needs to be odd.

 

The reason 2 is the only even prime number is that all even numbers have 2 as a divisor. Since a prime number can have only 1 and itself as a divisor, two can be the only even prime. The same would be true, for example, with the number 3. Three is the only multiple of 3 that is prime just as 2 is the only multiple of 2 that is prime.

 

Division, on the other hand, is typically defined (at least, in basic natural number arithmetic) as the inverse of multiplication,

 

...Division is the inverse operation of multiplication...

 

http://mathworld.wolfram.com/Division.html

 

which actually places x/0 outside the definition of "division".

 

~modest

[Don Blazys]

The equation 6/3=2 implies the true statement 2*3=6. Therefore, the expression 6/3 is allowed.

 

Likewise, 0/0=N implies the true statement N*0=0. Therefore, the expression 0/0 is also allowed,

 

even though it is indeterminate.

 

However, 6/0=N implies the false statement N*0=6. Therefore, the expression 6/0 is strictly disallowed

 

because it is both impossible and nonsensical.

 

Don.

[Qfwfq]

I see what you're saying here, doing multiplication backwards to get division, but remember: There are many exceptions to rules in math. for example, It is safe to say any even number is not prime. except for 2, the one and only exception to the rule. See what I mean? Also, you said that you put zero cookies in the first group, but at that point you had allready gone too far. you weren't supposed to make one, two, three, or more groups, just 0.

No prime except 7 can be a multiple of 7.

 

No prime except 31 can be a multiple of 31.

 

Even is just a way of saying multiple of 2 and 2 is the lowest prime.

[CraigD]

Well to start off let me say what division is. I'm quite sure it literally means: to take X and spread it out among Y groups. Even though it can is often said as "how many times X goes into Y", im quite sure that is technically incorrect.

...

Using the first method (of division), 15/0 = 0, because 15 spread out equally among no groups would yield nothing. Using the second method, the equation would read 15/0 = infinity. So why is it regarded as impossible, when 15 spread out equally accross 0 groups clearly equals 0?

As you’ve already been informed, Zac, by almost exceptionless consensus of pro and amateur math folk alike division by zero produces not 0 but an indeterminate – that is, a number without a knowable value. It’s good, I think, to recognize that operations, such as division, are really just rules for producing numbers, so we don’t need to be bound by them when they’re not useful, or feel that the division operator must be a particular rule and no other. So, if you want [imath]n \div 0 = 0[/imath], you can redefine the division operation so that this is true, so long as you are clear that it is not the usual operator.

 

I think, however, there are strong reasons such an alternate division operation hasn’t been widely used. A major one that comes to mind is continuity, a central and very useful mathematical concept. In the context of division, as a divisor becomes smaller, the result of division becomes larger. Thus a fairly popular alternative division operator has [imath]n \div 0 = \infty[/imath]. Such a definition requires a number system that includes infinity, but these aren’t uncommon, and are useful. This allows the continuity of the division operator to be preserved for division by zero, and remains compatible with the usual [imath]n \div 0 \,\mbox{is indeterminate}[/imath] definition, as infinity is indeterminate in number systems that don’t include it.

 

Defining division such that [imath]n \div 0 = 0[/imath] results in a situation where, the result of the division becomes larger as the divisor gets bigger, until the divisor reaches zero, and the result becomes the smallest number, zero. This is an ugly and troubling lack of continuity.