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Zero Divided By Zero

DevinKing
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11/9/2011 8:42:55 PM
Posted: 5 years ago
--I have recently gotten into a dispute over what the value of zero divided by zero is, if it is in fact something that can be determined. It is my view that it is equal to zero, although my math teacher disagrees by saying that it is indeterminate.

--My reasoning is as follows: Division is simply repeated subtraction of a certain number from another given number until it reaches zero. The number of time that this subtraction needs to be done is the answer. Ex: 10/2=5 since 2 must be subtracted from ten 5 times until zero is reached. This is why 0/7=0 since it is not necessary to subtract 7 at all in order to reach zero. As such, I would expect it to follow that 0/0=0 since it is equally unnecessary to perform any subtraction being that the starting number is zero. However, every source I look up says that the answer is indeterminate. So I ask where I am going wrong in my reasoning if that be the case?
After demonstrating his existence with complete certainty with the proposition "I think, therefore I am", Descartes walks into a bar, sitting next to a gorgeous priest. The priest asks Descartes, "Would you like a drink?" Descartes responds, "I think not," and then proceeds to vanish in a puff of illogic.
000ike
Posts: 11,196
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11/9/2011 8:48:15 PM
Posted: 5 years ago
0/0 , if we are to subtract until the numerator is occupied and equals zero, then 0/0 is impossible. x/0 assumes that 0 is a VALUE, A THING that can be subtracted. It makes the statement that nothing can occupy something.

Nothing cannot occupy something. In the fraction 10/2,....2 occupies 10, 5 times. 0 is absence of something, therefore, nothing. Nothing cannot occupy something.
"A stupid despot may constrain his slaves with iron chains; but a true politician binds them even more strongly with the chain of their own ideas" - Michel Foucault
drafterman
Posts: 18,870
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11/9/2011 8:52:00 PM
Posted: 5 years ago
At 11/9/2011 8:42:55 PM, DevinKing wrote:
--I have recently gotten into a dispute over what the value of zero divided by zero is, if it is in fact something that can be determined. It is my view that it is equal to zero, although my math teacher disagrees by saying that it is indeterminate.

--My reasoning is as follows: Division is simply repeated subtraction of a certain number from another given number until it reaches zero. The number of time that this subtraction needs to be done is the answer. Ex: 10/2=5 since 2 must be subtracted from ten 5 times until zero is reached. This is why 0/7=0 since it is not necessary to subtract 7 at all in order to reach zero. As such, I would expect it to follow that 0/0=0 since it is equally unnecessary to perform any subtraction being that the starting number is zero. However, every source I look up says that the answer is indeterminate. So I ask where I am going wrong in my reasoning if that be the case?

0/0 = a
0 = 0*a
0 = 0

It results in a true statement regardless of the value of a. Hence 'indeterminate.'
000ike
Posts: 11,196
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11/9/2011 8:57:41 PM
Posted: 5 years ago
At 11/9/2011 8:52:00 PM, drafterman wrote:
At 11/9/2011 8:42:55 PM, DevinKing wrote:
--I have recently gotten into a dispute over what the value of zero divided by zero is, if it is in fact something that can be determined. It is my view that it is equal to zero, although my math teacher disagrees by saying that it is indeterminate.

--My reasoning is as follows: Division is simply repeated subtraction of a certain number from another given number until it reaches zero. The number of time that this subtraction needs to be done is the answer. Ex: 10/2=5 since 2 must be subtracted from ten 5 times until zero is reached. This is why 0/7=0 since it is not necessary to subtract 7 at all in order to reach zero. As such, I would expect it to follow that 0/0=0 since it is equally unnecessary to perform any subtraction being that the starting number is zero. However, every source I look up says that the answer is indeterminate. So I ask where I am going wrong in my reasoning if that be the case?

0/0 = a
0 = 0*a
0 = 0

It results in a true statement regardless of the value of a. Hence 'indeterminate.'

a has no value. A cannot have a value. It is indeterminate because a does not exist, not because a can be any value.
"A stupid despot may constrain his slaves with iron chains; but a true politician binds them even more strongly with the chain of their own ideas" - Michel Foucault
M.Torres
Posts: 3,626
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11/9/2011 8:59:53 PM
Posted: 5 years ago
At 11/9/2011 8:42:55 PM, DevinKing wrote:
--I have recently gotten into a dispute over what the value of zero divided by zero is, if it is in fact something that can be determined. It is my view that it is equal to zero, although my math teacher disagrees by saying that it is indeterminate.

--My reasoning is as follows: Division is simply repeated subtraction of a certain number from another given number until it reaches zero. The number of time that this subtraction needs to be done is the answer. Ex: 10/2=5 since 2 must be subtracted from ten 5 times until zero is reached. This is why 0/7=0 since it is not necessary to subtract 7 at all in order to reach zero. As such, I would expect it to follow that 0/0=0 since it is equally unnecessary to perform any subtraction being that the starting number is zero. However, every source I look up says that the answer is indeterminate. So I ask where I am going wrong in my reasoning if that be the case?

... what?

Division is just that. Division. Taking a number and splitting into certain separated groups of equal value. For example, your 10/2=5 means 10 divided into 2 equals groups of value, this value being 5. Therefore, you cannot divide by zero since you cannot put any number into groups that lack value since they ARE values themselves.
: At 11/28/2011 1:28:24 PM, BlackVoid wrote:
: M. Torres said it, so it must be right.

I'm an Apatheistic Ignostic. ... problem? ;D

I believe in the heart of the cards. .:DDO Duelist:.
000ike
Posts: 11,196
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11/9/2011 9:01:29 PM
Posted: 5 years ago
At 11/9/2011 8:59:53 PM, M.Torres wrote:
At 11/9/2011 8:42:55 PM, DevinKing wrote:
--I have recently gotten into a dispute over what the value of zero divided by zero is, if it is in fact something that can be determined. It is my view that it is equal to zero, although my math teacher disagrees by saying that it is indeterminate.

--My reasoning is as follows: Division is simply repeated subtraction of a certain number from another given number until it reaches zero. The number of time that this subtraction needs to be done is the answer. Ex: 10/2=5 since 2 must be subtracted from ten 5 times until zero is reached. This is why 0/7=0 since it is not necessary to subtract 7 at all in order to reach zero. As such, I would expect it to follow that 0/0=0 since it is equally unnecessary to perform any subtraction being that the starting number is zero. However, every source I look up says that the answer is indeterminate. So I ask where I am going wrong in my reasoning if that be the case?

... what?

Division is just that. Division. Taking a number and splitting into certain separated groups of equal value. For example, your 10/2=5 means 10 divided into 2 equals groups of value, this value being 5. Therefore, you cannot divide by zero since you cannot put any number into groups that lack value since they ARE values themselves.

Yep. This is correct. Nothing cannot occupy something.
"A stupid despot may constrain his slaves with iron chains; but a true politician binds them even more strongly with the chain of their own ideas" - Michel Foucault
M.Torres
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11/9/2011 9:01:51 PM
Posted: 5 years ago
At 11/9/2011 8:59:53 PM, M.Torres wrote:
At 11/9/2011 8:42:55 PM, DevinKing wrote:
--I have recently gotten into a dispute over what the value of zero divided by zero is, if it is in fact something that can be determined. It is my view that it is equal to zero, although my math teacher disagrees by saying that it is indeterminate.

--My reasoning is as follows: Division is simply repeated subtraction of a certain number from another given number until it reaches zero. The number of time that this subtraction needs to be done is the answer. Ex: 10/2=5 since 2 must be subtracted from ten 5 times until zero is reached. This is why 0/7=0 since it is not necessary to subtract 7 at all in order to reach zero. As such, I would expect it to follow that 0/0=0 since it is equally unnecessary to perform any subtraction being that the starting number is zero. However, every source I look up says that the answer is indeterminate. So I ask where I am going wrong in my reasoning if that be the case?

... what?

Division is just that. Division. Taking a number and splitting into certain separated groups of equal value. For example, your 10/2=5 means 10 divided into 2 equals groups of value, this value being 5. Therefore, you cannot divide by zero since you cannot put any number into groups that lack value since they ARE values themselves.

Therefore, if you divide 0 by 0, you are trying to split the lack of value into equal groups of value. You cannot do this, therefore, indeterminate. You cannot determine the equal values of the lack of value being split, in the same way you cannot split a value into groups that lack value, equally.
: At 11/28/2011 1:28:24 PM, BlackVoid wrote:
: M. Torres said it, so it must be right.

I'm an Apatheistic Ignostic. ... problem? ;D

I believe in the heart of the cards. .:DDO Duelist:.
drafterman
Posts: 18,870
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11/9/2011 9:09:00 PM
Posted: 5 years ago
At 11/9/2011 8:57:41 PM, 000ike wrote:
At 11/9/2011 8:52:00 PM, drafterman wrote:
At 11/9/2011 8:42:55 PM, DevinKing wrote:
--I have recently gotten into a dispute over what the value of zero divided by zero is, if it is in fact something that can be determined. It is my view that it is equal to zero, although my math teacher disagrees by saying that it is indeterminate.

--My reasoning is as follows: Division is simply repeated subtraction of a certain number from another given number until it reaches zero. The number of time that this subtraction needs to be done is the answer. Ex: 10/2=5 since 2 must be subtracted from ten 5 times until zero is reached. This is why 0/7=0 since it is not necessary to subtract 7 at all in order to reach zero. As such, I would expect it to follow that 0/0=0 since it is equally unnecessary to perform any subtraction being that the starting number is zero. However, every source I look up says that the answer is indeterminate. So I ask where I am going wrong in my reasoning if that be the case?

0/0 = a
0 = 0*a
0 = 0

It results in a true statement regardless of the value of a. Hence 'indeterminate.'

a has no value. A cannot have a value. It is indeterminate because a does not exist, not because a can be any value.

A can most certainly have a value, just plug one in.

0 = 0*1
0 = 0*2
0 = 0*3
...

The equation is true for any value of 'a'
http://mathforum.org...
000ike
Posts: 11,196
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11/9/2011 9:15:09 PM
Posted: 5 years ago
At 11/9/2011 9:09:00 PM, drafterman wrote:
At 11/9/2011 8:57:41 PM, 000ike wrote:
At 11/9/2011 8:52:00 PM, drafterman wrote:
At 11/9/2011 8:42:55 PM, DevinKing wrote:
--I have recently gotten into a dispute over what the value of zero divided by zero is, if it is in fact something that can be determined. It is my view that it is equal to zero, although my math teacher disagrees by saying that it is indeterminate.

--My reasoning is as follows: Division is simply repeated subtraction of a certain number from another given number until it reaches zero. The number of time that this subtraction needs to be done is the answer. Ex: 10/2=5 since 2 must be subtracted from ten 5 times until zero is reached. This is why 0/7=0 since it is not necessary to subtract 7 at all in order to reach zero. As such, I would expect it to follow that 0/0=0 since it is equally unnecessary to perform any subtraction being that the starting number is zero. However, every source I look up says that the answer is indeterminate. So I ask where I am going wrong in my reasoning if that be the case?

0/0 = a
0 = 0*a
0 = 0

It results in a true statement regardless of the value of a. Hence 'indeterminate.'

a has no value. A cannot have a value. It is indeterminate because a does not exist, not because a can be any value.

A can most certainly have a value, just plug one in.

0 = 0*1
0 = 0*2
0 = 0*3
...

The equation is true for any value of 'a'
http://mathforum.org...

uh, no. The equation was 0/0 = a. You cannot give "a" a value. A = undefined, it does not exist. What you're doing is multiplying by a nonexistent variable, 0 = 0(a) does not translate into 0=0 because that is an impossible and unusable equation.

The simplification stops when you get to 0 = 0a. It does not dissolve into 0 = 0. This is where you're wrong.

Trust me, this is how its viewed everywhere in the world.
"A stupid despot may constrain his slaves with iron chains; but a true politician binds them even more strongly with the chain of their own ideas" - Michel Foucault
000ike
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11/9/2011 9:17:33 PM
Posted: 5 years ago
Heck, what am I saying. Get rid of "a" all together. A variable ASSUMES value. There is no such thing as a valueless variable. Therefore 0/0 = a is a mathematical impossibility. 0/0 = undefined.
"A stupid despot may constrain his slaves with iron chains; but a true politician binds them even more strongly with the chain of their own ideas" - Michel Foucault
mattrodstrom
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11/9/2011 9:17:42 PM
Posted: 5 years ago
I tend to think of it like this

When I say: what's x divided by Y

I mean: how many times does Y go into X..

and when you think about it this way...

0/0 = infinity... and 1/0 = infinity
"He who does not know how to put his will into things at least puts a meaning into them: that is, he believes there is a will in them already."

Metaphysics:
"The science.. which deals with the fundamental errors of mankind - but as if they were the fundamental truths."
DevinKing
Posts: 206
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11/9/2011 9:19:00 PM
Posted: 5 years ago
At 11/9/2011 8:52:00 PM, drafterman wrote:
0/0 = a
0 = 0*a
0 = 0

It results in a true statement regardless of the value of a. Hence 'indeterminate.'

--There is one objection to the use of this proof (this is the proof offered by every legitimate source) That is that this problem is of a special nature which cannot be resolved by this algebraic means. The reason behind this is that no algebraic equation can be solved by the multiplication of zero to both sides as this will always result in 0=0. Think of 2x+1=x. If we multiply both sides by zero, then we come to a true statement: 0=0. The zero's status in the case in question as the denominator does not exempt this equation from this effect. On these grounds I reject this as a proof, although I am more than open to correction if I have made an error.

--For further demonstration of my point:

1=2
0*1=2*0
0=0
After demonstrating his existence with complete certainty with the proposition "I think, therefore I am", Descartes walks into a bar, sitting next to a gorgeous priest. The priest asks Descartes, "Would you like a drink?" Descartes responds, "I think not," and then proceeds to vanish in a puff of illogic.
drafterman
Posts: 18,870
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11/9/2011 9:22:06 PM
Posted: 5 years ago
At 11/9/2011 9:15:09 PM, 000ike wrote:
At 11/9/2011 9:09:00 PM, drafterman wrote:
At 11/9/2011 8:57:41 PM, 000ike wrote:
At 11/9/2011 8:52:00 PM, drafterman wrote:
At 11/9/2011 8:42:55 PM, DevinKing wrote:
--I have recently gotten into a dispute over what the value of zero divided by zero is, if it is in fact something that can be determined. It is my view that it is equal to zero, although my math teacher disagrees by saying that it is indeterminate.

--My reasoning is as follows: Division is simply repeated subtraction of a certain number from another given number until it reaches zero. The number of time that this subtraction needs to be done is the answer. Ex: 10/2=5 since 2 must be subtracted from ten 5 times until zero is reached. This is why 0/7=0 since it is not necessary to subtract 7 at all in order to reach zero. As such, I would expect it to follow that 0/0=0 since it is equally unnecessary to perform any subtraction being that the starting number is zero. However, every source I look up says that the answer is indeterminate. So I ask where I am going wrong in my reasoning if that be the case?

0/0 = a
0 = 0*a
0 = 0

It results in a true statement regardless of the value of a. Hence 'indeterminate.'

a has no value. A cannot have a value. It is indeterminate because a does not exist, not because a can be any value.

A can most certainly have a value, just plug one in.

0 = 0*1
0 = 0*2
0 = 0*3
...

The equation is true for any value of 'a'
http://mathforum.org...

uh, no. The equation was 0/0 = a. You cannot give "a" a value. A = undefined, it does not exist. What you're doing is multiplying by a nonexistent variable, 0 = 0(a) does not translate into 0=0 because that is an impossible and unusable equation.

The simplification stops when you get to 0 = 0a. It does not dissolve into 0 = 0. This is where you're wrong.

Trust me, this is how its viewed everywhere in the world.

Except, you know, the link I provide. It's simple algebra.

Since 0 times anything equals zero, simple substitution allows me to go from

0 = 0*a

to

0 = 0
000ike
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11/9/2011 9:22:52 PM
Posted: 5 years ago
At 11/9/2011 9:17:42 PM, mattrodstrom wrote:
I tend to think of it like this

When I say: what's x divided by Y

I mean: how many times does Y go into X..

and when you think about it this way...

0/0 = infinity... and 1/0 = infinity

infinity is all numbers. 0/0 = nothing (undefined). 0 cannot go into 0, so if you were to set up the sentence, 0 goes into 0 _____ times, you would have to stop because that sentence is absurd. You feel temted to fill that blank with a 0, but if you remember 0 is still equal to NOTHING. Nothing cannot occupy something. Nothing cannot occupy nothing. Only something can occupy nothing and something occupy something. hence 0/9 , 1/9 = possible ----- 9/0, 0/0 = impossible
"A stupid despot may constrain his slaves with iron chains; but a true politician binds them even more strongly with the chain of their own ideas" - Michel Foucault
drafterman
Posts: 18,870
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11/9/2011 9:23:34 PM
Posted: 5 years ago
At 11/9/2011 9:19:00 PM, DevinKing wrote:
At 11/9/2011 8:52:00 PM, drafterman wrote:
0/0 = a
0 = 0*a
0 = 0

It results in a true statement regardless of the value of a. Hence 'indeterminate.'

--There is one objection to the use of this proof (this is the proof offered by every legitimate source) That is that this problem is of a special nature which cannot be resolved by this algebraic means. The reason behind this is that no algebraic equation can be solved by the multiplication of zero to both sides as this will always result in 0=0. Think of 2x+1=x. If we multiply both sides by zero, then we come to a true statement: 0=0. The zero's status in the case in question as the denominator does not exempt this equation from this effect. On these grounds I reject this as a proof, although I am more than open to correction if I have made an error.

--For further demonstration of my point:

1=2
0*1=2*0
0=0

This makes more sense as an objection. Thanks.
DevinKing
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11/9/2011 9:43:40 PM
Posted: 5 years ago
At 11/9/2011 8:59:53 PM, M.Torres wrote::
... what?

Division is just that. Division. Taking a number and splitting into certain separated groups of equal value. For example, your 10/2=5 means 10 divided into 2 equals groups of value, this value being 5. Therefore, you cannot divide by zero since you cannot put any number into groups that lack value since they ARE values themselves.

--Then I must raise the question, what do you believe the value of something is once it is divided by zero? The prevailing view is that it is undefined, which is synonymous with +/- infinite.
After demonstrating his existence with complete certainty with the proposition "I think, therefore I am", Descartes walks into a bar, sitting next to a gorgeous priest. The priest asks Descartes, "Would you like a drink?" Descartes responds, "I think not," and then proceeds to vanish in a puff of illogic.
mattrodstrom
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11/9/2011 9:49:14 PM
Posted: 5 years ago
At 11/9/2011 9:22:52 PM, 000ike wrote:
At 11/9/2011 9:17:42 PM, mattrodstrom wrote:
I tend to think of it like this

When I say: what's x divided by Y

I mean: how many times does Y go into X..

and when you think about it this way...

0/0 = infinity... and 1/0 = infinity

infinity is all numbers. 0/0 = nothing (undefined). 0 cannot go into 0, so if you were to set up the sentence, 0 goes into 0 _____ times, you would have to stop because that sentence is absurd. You feel temted to fill that blank with a 0, but if you remember 0 is still equal to NOTHING. Nothing cannot occupy something. Nothing cannot occupy nothing. Only something can occupy nothing and something occupy something. hence 0/9 , 1/9 = possible ----- 9/0, 0/0 = impossible

they're abstract numbers.. not concrete somethings.

your talk of them as concrete somethings doesn't explain why 0/10 = 0

It simply makes No Sense to say what you did before: "something can occupy nothing"

Given this.. it would seem that according to your line of explanation 0/10 should be undefined Too.

My explanation doesn't do this.. and so generally seems to match the common meaning better ;)

here it is:
In multiplying X times y [ when x=10 , y= 0]...
you're saying count X, y times... 10, 0 times
in dividing y/x you're saying how many times does x go into y? how many times does 10 go into 0??
the answer is 0 times.

If you divide x/y.. you're asking how many times does y go into x? how many times does 0 go into 10... the answer is Infinite times!.. Easily!

with 10/2 the answer is 2 goes into 10 exactly 5 times...

with 10/0.. well.. 0 goes into 10 Endlessly.. infinitely.. no prob.
"He who does not know how to put his will into things at least puts a meaning into them: that is, he believes there is a will in them already."

Metaphysics:
"The science.. which deals with the fundamental errors of mankind - but as if they were the fundamental truths."
M.Torres
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11/9/2011 9:52:04 PM
Posted: 5 years ago
At 11/9/2011 9:43:40 PM, DevinKing wrote:
At 11/9/2011 8:59:53 PM, M.Torres wrote::
... what?

Division is just that. Division. Taking a number and splitting into certain separated groups of equal value. For example, your 10/2=5 means 10 divided into 2 equals groups of value, this value being 5. Therefore, you cannot divide by zero since you cannot put any number into groups that lack value since they ARE values themselves.

--Then I must raise the question, what do you believe the value of something is once it is divided by zero? The prevailing view is that it is undefined, which is synonymous with +/- infinite.

Something divided by 0 is a value divided into equal groups of a lack of value. You CANNOT make that which has value equally distribute into groups that lack value. Therefore, this is why you cannot divide by zero. I believe I already explained this in an earlier post.

How is that infinite? It merely does not exist.
: At 11/28/2011 1:28:24 PM, BlackVoid wrote:
: M. Torres said it, so it must be right.

I'm an Apatheistic Ignostic. ... problem? ;D

I believe in the heart of the cards. .:DDO Duelist:.
M.Torres
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11/9/2011 9:53:37 PM
Posted: 5 years ago
At 11/9/2011 9:52:04 PM, M.Torres wrote:
At 11/9/2011 9:43:40 PM, DevinKing wrote:
At 11/9/2011 8:59:53 PM, M.Torres wrote::
... what?

Division is just that. Division. Taking a number and splitting into certain separated groups of equal value. For example, your 10/2=5 means 10 divided into 2 equals groups of value, this value being 5. Therefore, you cannot divide by zero since you cannot put any number into groups that lack value since they ARE values themselves.

--Then I must raise the question, what do you believe the value of something is once it is divided by zero? The prevailing view is that it is undefined, which is synonymous with +/- infinite.

Something divided by 0 is a value divided into equal groups of a lack of value. You CANNOT make that which has value equally distribute into groups that lack value. Therefore, this is why you cannot divide by zero. I believe I already explained this in an earlier post.

How is that infinite? It merely does not exist.

Hm. Actually, I'm wrong. It would be that the number is equal to infinite amounts of groups that lack value, but inherently that does not exist in the way infinity does not exist.
: At 11/28/2011 1:28:24 PM, BlackVoid wrote:
: M. Torres said it, so it must be right.

I'm an Apatheistic Ignostic. ... problem? ;D

I believe in the heart of the cards. .:DDO Duelist:.
DevinKing
Posts: 206
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11/9/2011 9:55:20 PM
Posted: 5 years ago
--I have always thought of multiplication in terms of repeated addition, and division, being the opposite, in terms of repeated subtraction. This works without doubt on the vast majority of problems but as it turns out, raises objections on this one particular issue of zero.

--The only difference is that one definition provides a value for division problems involving zero and the other doesn't.

--Another observation: using the definition of division as "placing the given number into another certain number of equal groups with the value a group being the answer," then division of zero by any number is also absurd since zero cannot be manipulated to form groups.
After demonstrating his existence with complete certainty with the proposition "I think, therefore I am", Descartes walks into a bar, sitting next to a gorgeous priest. The priest asks Descartes, "Would you like a drink?" Descartes responds, "I think not," and then proceeds to vanish in a puff of illogic.
M.Torres
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11/9/2011 9:57:37 PM
Posted: 5 years ago
At 11/9/2011 9:55:20 PM, DevinKing wrote:
--I have always thought of multiplication in terms of repeated addition, and division, being the opposite, in terms of repeated subtraction. This works without doubt on the vast majority of problems but as it turns out, raises objections on this one particular issue of zero.

Which is why you need to rethink how you're viewing it.


--The only difference is that one definition provides a value for division problems involving zero and the other doesn't.

Which is the definition you haven't been able to prove...?


--Another observation: using the definition of division as "placing the given number into another certain number of equal groups with the value a group being the answer," then division of zero by any number is also absurd since zero cannot be manipulated to form groups.

Which is why if you divide 0 by something, it is 0...
: At 11/28/2011 1:28:24 PM, BlackVoid wrote:
: M. Torres said it, so it must be right.

I'm an Apatheistic Ignostic. ... problem? ;D

I believe in the heart of the cards. .:DDO Duelist:.
DevinKing
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11/9/2011 9:59:43 PM
Posted: 5 years ago
At 11/9/2011 9:53:37 PM, M.Torres wrote:
At 11/9/2011 9:52:04 PM, M.Torres wrote:
At 11/9/2011 9:43:40 PM, DevinKing wrote:
At 11/9/2011 8:59:53 PM, M.Torres wrote::
... what?

Division is just that. Division. Taking a number and splitting into certain separated groups of equal value. For example, your 10/2=5 means 10 divided into 2 equals groups of value, this value being 5. Therefore, you cannot divide by zero since you cannot put any number into groups that lack value since they ARE values themselves.

--Then I must raise the question, what do you believe the value of something is once it is divided by zero? The prevailing view is that it is undefined, which is synonymous with +/- infinite.

Something divided by 0 is a value divided into equal groups of a lack of value. You CANNOT make that which has value equally distribute into groups that lack value. Therefore, this is why you cannot divide by zero. I believe I already explained this in an earlier post.

How is that infinite? It merely does not exist.

Hm. Actually, I'm wrong. It would be that the number is equal to infinite amounts of groups that lack value, but inherently that does not exist in the way infinity does not exist.

--The problem though, is that if you accept that it is an infinite number of groups with no value, then 1/0=infinity. This is because the answer to division is the number of groups using your definition.
After demonstrating his existence with complete certainty with the proposition "I think, therefore I am", Descartes walks into a bar, sitting next to a gorgeous priest. The priest asks Descartes, "Would you like a drink?" Descartes responds, "I think not," and then proceeds to vanish in a puff of illogic.
M.Torres
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11/9/2011 10:02:04 PM
Posted: 5 years ago
At 11/9/2011 9:59:43 PM, DevinKing wrote:
At 11/9/2011 9:53:37 PM, M.Torres wrote:
At 11/9/2011 9:52:04 PM, M.Torres wrote:
At 11/9/2011 9:43:40 PM, DevinKing wrote:
At 11/9/2011 8:59:53 PM, M.Torres wrote::
... what?

Division is just that. Division. Taking a number and splitting into certain separated groups of equal value. For example, your 10/2=5 means 10 divided into 2 equals groups of value, this value being 5. Therefore, you cannot divide by zero since you cannot put any number into groups that lack value since they ARE values themselves.

--Then I must raise the question, what do you believe the value of something is once it is divided by zero? The prevailing view is that it is undefined, which is synonymous with +/- infinite.

Something divided by 0 is a value divided into equal groups of a lack of value. You CANNOT make that which has value equally distribute into groups that lack value. Therefore, this is why you cannot divide by zero. I believe I already explained this in an earlier post.

How is that infinite? It merely does not exist.

Hm. Actually, I'm wrong. It would be that the number is equal to infinite amounts of groups that lack value, but inherently that does not exist in the way infinity does not exist.

--The problem though, is that if you accept that it is an infinite number of groups with no value, then 1/0=infinity. This is because the answer to division is the number of groups using your definition.

What it means is that you cannot divide 1 by 0. As you cannot divide ANY number by 0. Try it on a calculator, and you'll see IT DOES NOT WORK. It results in infinity, which is an undefinable number. How is this a "problem"?
: At 11/28/2011 1:28:24 PM, BlackVoid wrote:
: M. Torres said it, so it must be right.

I'm an Apatheistic Ignostic. ... problem? ;D

I believe in the heart of the cards. .:DDO Duelist:.
Man-is-good
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11/9/2011 10:19:39 PM
Posted: 5 years ago
At 11/9/2011 9:09:00 PM, drafterman wrote:
At 11/9/2011 8:57:41 PM, 000ike wrote:
At 11/9/2011 8:52:00 PM, drafterman wrote:
At 11/9/2011 8:42:55 PM, DevinKing wrote:
--I have recently gotten into a dispute over what the value of zero divided by zero is, if it is in fact something that can be determined. It is my view that it is equal to zero, although my math teacher disagrees by saying that it is indeterminate.

--My reasoning is as follows: Division is simply repeated subtraction of a certain number from another given number until it reaches zero. The number of time that this subtraction needs to be done is the answer. Ex: 10/2=5 since 2 must be subtracted from ten 5 times until zero is reached. This is why 0/7=0 since it is not necessary to subtract 7 at all in order to reach zero. As such, I would expect it to follow that 0/0=0 since it is equally unnecessary to perform any subtraction being that the starting number is zero. However, every source I look up says that the answer is indeterminate. So I ask where I am going wrong in my reasoning if that be the case?

0/0 = a
0 = 0*a
0 = 0

It results in a true statement regardless of the value of a. Hence 'indeterminate.'

a has no value. A cannot have a value. It is indeterminate because a does not exist, not because a can be any value.

A can most certainly have a value, just plug one in.

0 = 0*1
0 = 0*2
0 = 0*3
...

The equation is true for any value of 'a'
http://mathforum.org...

But then a could equal a wide set of values, making it indeterminate...
"Homo sum, humani nihil a me alienum puto." --Terence

"I believe that the mind can be permanently profaned by the habit of attending to trivial things, so that all our thoughts shall be tinged with triviality."--Thoreau
DevinKing
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11/9/2011 10:38:33 PM
Posted: 5 years ago
At 11/9/2011 10:02:04 PM, M.Torres wrote:
At 11/9/2011 9:59:43 PM, DevinKing wrote:

--The problem though, is that if you accept that it is an infinite number of groups with no value, then 1/0=infinity. This is because the answer to division is the number of groups using your definition.

What it means is that you cannot divide 1 by 0. As you cannot divide ANY number by 0. Try it on a calculator, and you'll see IT DOES NOT WORK. It results in infinity, which is an indefinable number. How is this a "problem"?

--It's a problem for you because it demonstrates my definition of division to be superior. The answer of infinity cannot be reached through your definition of division. The only way which comes to this conclusion that I have seen presented here is the concept of division as repeated subtraction. 1 divided into 0 groups is Zero by your definition since the value of a group would not exist in the absence of any groups, in other words, there isn't a single group which has a value of infinity by that way of thinking.

--Understand this: The two methods of defining division break down into the answer being the number of groups (10/2 yields 5 groups with a value of 2 in each group) or the value of any one of these equal groups (10/2 yields 2 groups with a value of 5 in each group). My subtraction method is the former while the method you are using is the latter. While both methods work under normal circumstances and seem equally plausible (you can indeed break 10 down evenly using both ways), the latter method fails in the face of the 1/0 question. This is because there is no group which can have its value measured at all. It has, by definition, no groups. You cannot logically divide something into zero groups and then use the value of this nonexistent group as your answer.

--The two methods may be more easily stated as 10/2 put into a question:

1. How many groups of 2 can be in 10? Answer: 5.
2. How much is in each group if 10 is put into 2 groups? Answer: 5.

Or 1/0 restated:

1. How many groups of 0 can be in 1? Answer: An infinite amount.
2. How much is in each group if 1 is put into 0 groups? Answer: There are no groups.

--Now think of 0/0.

1. How many groups of 0 can be in 0? Answer: 0; there is nothing to put into groups (even groups of zero).
2. How much is in each group if 0 is put into 0 groups? Answer: There are no groups.

--I certainly hope this cleared up some of my reasoning.
After demonstrating his existence with complete certainty with the proposition "I think, therefore I am", Descartes walks into a bar, sitting next to a gorgeous priest. The priest asks Descartes, "Would you like a drink?" Descartes responds, "I think not," and then proceeds to vanish in a puff of illogic.
Chuz-Life
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11/10/2011 8:00:59 PM
Posted: 5 years ago
"Nothing from nothing leaves nothing"

In my view, to "divide by zero" is the same thing as "not dividing at all."

7/0 = 0 because the "7" is "undivided" (not divided)

Therefore 0/0= 0

Same as zero minus zero equals zero.

Division is just another form of subtraction. Right?

(0/0) = (0-0)

Problem solved.
"Sooner or later, the Supreme Court of the Unites States is going to have explain how a 'child in the womb' is a person enough to be recognized as a MURDER victim under our fetal homicide laws but how they are not persons enough to qualify for any other Constitutional protections" ~ Chuz Life

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drafterman
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11/10/2011 8:04:00 PM
Posted: 5 years ago
At 11/10/2011 8:00:59 PM, Chuz-Life wrote:
"Nothing from nothing leaves nothing"

In my view, to "divide by zero" is the same thing as "not dividing at all."

7/0 = 0 because the "7" is "undivided" (not divided)

Therefore 0/0= 0

Same as zero minus zero equals zero.

Division is just another form of subtraction. Right?

(0/0) = (0-0)

Problem solved.

Dividing by 1 is "not dividing at all"
Chuz-Life
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11/10/2011 8:24:17 PM
Posted: 5 years ago
At 11/10/2011 8:04:00 PM, drafterman wrote:
At 11/10/2011 8:00:59 PM, Chuz-Life wrote:
"Nothing from nothing leaves nothing"

In my view, to "divide by zero" is the same thing as "not dividing at all."

7/0 = 0 because the "7" is "undivided" (not divided)

Therefore 0/0= 0

Same as zero minus zero equals zero.

Division is just another form of subtraction. Right?

(0/0) = (0-0)

Problem solved.

Dividing by 1 is "not dividing at all"

Matter of perspective
"Sooner or later, the Supreme Court of the Unites States is going to have explain how a 'child in the womb' is a person enough to be recognized as a MURDER victim under our fetal homicide laws but how they are not persons enough to qualify for any other Constitutional protections" ~ Chuz Life

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drafterman
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11/10/2011 8:25:24 PM
Posted: 5 years ago
At 11/10/2011 8:24:17 PM, Chuz-Life wrote:
At 11/10/2011 8:04:00 PM, drafterman wrote:
At 11/10/2011 8:00:59 PM, Chuz-Life wrote:
"Nothing from nothing leaves nothing"

In my view, to "divide by zero" is the same thing as "not dividing at all."

7/0 = 0 because the "7" is "undivided" (not divided)

Therefore 0/0= 0

Same as zero minus zero equals zero.

Division is just another form of subtraction. Right?

(0/0) = (0-0)

Problem solved.

Dividing by 1 is "not dividing at all"

Matter of perspective

Uhm... not really. Take a pizza. Divide by one. You still have a whole pizza. Nothing's been divided.
Chuz-Life
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11/10/2011 8:32:17 PM
Posted: 5 years ago
At 11/10/2011 8:25:24 PM, drafterman wrote:
At 11/10/2011 8:24:17 PM, Chuz-Life wrote:
At 11/10/2011 8:04:00 PM, drafterman wrote:
At 11/10/2011 8:00:59 PM, Chuz-Life wrote:
"Nothing from nothing leaves nothing"

In my view, to "divide by zero" is the same thing as "not dividing at all."

7/0 = 0 because the "7" is "undivided" (not divided)

Therefore 0/0= 0

Same as zero minus zero equals zero.

Division is just another form of subtraction. Right?

(0/0) = (0-0)

Problem solved.

Dividing by 1 is "not dividing at all"

Matter of perspective

Uhm... not really. Take a pizza. Divide by one. You still have a whole pizza. Nothing's been divided.

I see your point,.... but logically and mathematically, a pizza divided by itself remains the whole. Despite the apprearances, the pizza was (logically) divided.... You just can't tell by looking at it.

When the same pizza is "divided by zero" is was neither physically not logically nor mathematically divided at all.... and while it my appear no different than a pizza that was divided by "one" we still know the difference between dividing it by one and not dividing it at all. :)
"Sooner or later, the Supreme Court of the Unites States is going to have explain how a 'child in the womb' is a person enough to be recognized as a MURDER victim under our fetal homicide laws but how they are not persons enough to qualify for any other Constitutional protections" ~ Chuz Life

http://www.debate.org...