Division By Zero

[scherado]

We all know from school, possibly long ago, that we can't divide by zero.

 

The browser tab identification is: "Science Forums"; (never mind the grammatical issue.) This should be easy.

 

What is the reason that we can't divide by zero?

[Crasto]

Feelings do..

Any movement in the unnuterable does...

Divide by zero seems to be something unnutarable and worth for nothing;

yet, nothing is the door...

Above all I believe in the power of the fraction (...the reason for)

So I admit the following:

-D/0= (( negative infinite -unusefull?

+D/= )) positive infinite    - useless?

0/0= () a singularity         - a nonesense?

Is infinite real? Or have we a problem of freedom here?...

[exchemist]

Feelings do..

Any movement in the unnuterable does...

Divide by zero seems to be something unnutarable and worth for nothing;

yet, nothing is the door...

Above all I believe in the power of the fraction (...the reason for)

So I admit the following:

-D/0= (( negative infinite -unusefull?

+D/= )) positive infinite    - useless?

0/0= () a singularity         - a nonesense?

Is infinite real? Or have we a problem of freedom here?...

Shouldn't that be un-nutterable? 

[scherado]

Feelings do..

Any movement in the unnuterable does...

Divide by zero seems to be something unnutarable and worth for nothing;

yet, nothing is the door...

Above all I believe in the power of the fraction (...the reason for)

So I admit the following:

-D/0= (( negative infinite -unusefull?

+D/= )) positive infinite    - useless?

0/0= () a singularity         - a nonesense?

Is infinite real? Or have we a problem of freedom here?...

.

B+!!!!!!! Excellent.

 

You almost got it Sparkie!!!

Edited September 18, 2017 by scherado

[sanctus]

One way to see it is A/B=C implies A=C*B

So 10/2=5 implies 10=5*2

And 10/0=x implies 10=x*0

And multiplication by 0 gives 0  unless x=infinity but then it is undefined

[DrKrettin]

Let x = y

 

xy = y^2

 

x^2 - xy = x^2 - y^2

 

x.(x - y) = (x + y)(x - y)

 

x = x + y

 

x = 2x

 

1 = 2

[Maine farmer]

Is the OP hinting at a question of the validity of the concept of the infinite?  

[scherado]

Is the OP hinting at a question of the validity of the concept of the infinite?

.

There is no ambiguity or controversy with respect to the reason division by zero is undefined, indeterminate or not permitted--choose your description--though there are few people with an accurate conception of infinity.

.

One way to see it is A/B=C implies A=C*B

 

So 10/2=5 implies 10=5*2

 

And 10/0=x implies 10=x*0

 

And multiplication by 0 gives 0 unless x=infinity but then it is undefined

.

For anybody: the bold in the above are not valid equations.

[sanctus]

Exactly, that is why I posted it, to show why it becomes undefined... Maybe did not word it nicely, should have said:

and if B=0 then it would become 10=x*0 which makes no sense ...

[scherado]

Exactly, that is why I posted it, to show why it becomes undefined...

.

No, not exactly, which is the entire thrust of the OP: your equations are not valid--specifically the right sides of them, but in the case of "0/0=", the quotient [fraction] itself is not valid.

 

----Edit---- I posted this reply in between your alteration of your post which I quote.

 

-----Edit 2---------------

 

Actually, now that I take a second look, 10/0 is not a valid fraction, which would make it invalid to be part of any equation.

.

...

And 10/0=x implies 10=x*0

...

Edited September 18, 2017 by scherado

[sanctus]

Again exactly my point 10/0 is not valid.

But if you hate it so much to see it, then just look at the valid side ;-), there is no x such that this equation holds
10=x*0

and hence this is what makes this 10/0 invalid.

[scherado]

Again exactly my point 10/0 is not valid.

 

But if you hate it so much to see it, then just look at the valid side ;-), there is no x such that this equation holds

10=x*0

 

and hence this is what makes this 10/0 invalid.

.

I don't hate to see it.

 

I ask again: What is the reason that we can't divide by zero? I ask again for the reason that you stated:

 

And 10/0=x implies...

 

If you agree that "10/0" is not valid, then it can't be part of that equation AND therefore, you never get to the part where it "implies" anything.

 

For the record, my answer to my question uses only words, though I don't assert that it can't be expressed with symbols.

 

-----------------Edit to add--------

 

I had an exchange with another guy elsewhere, where he stated:

.

In the loose expression 1/0 = infinity, the zero should be understood as some quantity ...

.

My response was: "Which of 1, 0 and "infinity" are quantities?"

Edited September 18, 2017 by scherado

[Maine farmer]

: "Which of 1, 0 and "infinity" are quantities?"

I would say that 1 is a quantity, 0 is the absence of quantity, and infinity is a concept of either increasing or decreasing without bounds.

[scherado]

I would say that 1 is a quantity, 0 is the absence of quantity, and infinity is a concept of either increasing or decreasing without bounds.

.

Yes, 1 is the only quantity of the three.

 

Of course, when I posted the question about "quantities", it was the giveaway hint--and I did it based on the fear that this thread could be locked at an moment on a whim. A puff of magic dragon.

 

We can't divide by zero for one reason: infinity is not a value.

 

There is mathematical infinity, which is everywhere, under every rock: Decimals between 0 and 1, integers ("increasing or decreasing without bounds"), real numbers -- the union set of rational and irrational numbers, which makes the choice of using the word "real" unfortunate. In advanced math, infinity is treated as a quanity to get past some roadblocks, if I remember correctly.

 

The illustration of inability to divide by zero is made by watching the value of a fraction when it's denominator decreases repeatedly.

 

3/1 = 3

3/.5 = 6

3/.25 = 12

3/.1 = 30

3/.01 = 300

 

One could reduce the denominator forever, approaching zero but never reaching zero. Putting the numbers to a graph X,Y the axis would extend forever and the graph can't be completed....which brings us to the "concept" of infinite distance.

 

There is the yet-to-be proved infinity of distance.

 

There is the possibility that existence is infinite, eternity: There was no beginning, relieving us of the problem of "before" the beginning.

[sanctus]

I see what you mean but isn't this exactly how you define something that is not valid?
You postulate something and see when it breaks down.
So let's postulate for any real A.B,C:
A/B=C because A=B*C

 

Then we test it until we find that it does not hold when B=0. So you have to postulate something new like
For any real A,B,C and B!=0:
A/B=C because A=B*C

[Crasto]

Because zero is a more a quality than a quantity, maybe is not correct to divide a quantity by a quality.

If we divide a quality by a quality let's enter 0/0, perhaps we get something in the order of density D, one possible reason for the different density of the positive and negative domains.

[scherado]

Because zero is a more a quality than a quantity, maybe is not correct to divide a quantity by a quality.

If we divide a quality by a quality let's enter 0/0, perhaps we get something in the order of density D, one possible reason for the different density of the positive and negative domains.

.

Not on this planet!!

.

I see what you mean but isn't this exactly how you define something that is not valid?

You postulate something and see when it breaks down.

So let's postulate for any real A.B,C:

A/B=C because A=B*C

 

Then we test it until we find that it does not hold when B=0. So you have to postulate something new like

For any real A,B,C and B!=0:

A/B=C because A=B*C

.

Does the above mean you dispute my answer? I can't make that determination. Perhaps, I need more food. I will read after lunch. It seems there's not much to add after:

.

.

Yes, 1 is the only quantity of the three.

 

Of course, when I posted the question about "quantities", it was the giveaway hint--and I did it based on the fear that this thread could be locked at an moment on a whim. A puff of magic dragon.

 

We can't divide by zero for one reason: infinity is not a value.

 

There is mathematical infinity, which is everywhere, under every rock: Decimals between 0 and 1, integers ("increasing or decreasing without bounds"), real numbers -- the union set of rational and irrational numbers, which makes the choice of using the word "real" unfortunate. In advanced math, infinity is treated as a quanity to get past some roadblocks, if I remember correctly.

 

The illustration of inability to divide by zero is made by watching the value of a fraction when it's denominator decreases repeatedly.

 

3/1 = 3

3/.5 = 6

3/.25 = 12

3/.1 = 30

3/.01 = 300

 

One could reduce the denominator forever, approaching zero but never reaching zero. Putting the numbers to a graph X,Y the axis would extend forever and the graph can't be completed....which brings us to the "concept" of infinite distance.

 

There is the yet-to-be proved infinity of distance.

 

There is the possibility that existence is infinite, eternity: There was no beginning, relieving us of the problem of "before" the beginning.

.

This is the reason I give my answer later than sooner.

Edited September 19, 2017 by scherado