[Yahya A.Sharif (OP)]

We have problems in physics that involve simple arithmetic such as division of two numbers, for example the speed v of an object at stationary equals zero, the time it elapses t is zero and the distance it ravels is also zero, however 0/0 is not defined and although its speed has a defined value which is zero.
Gravity at infinity equals zero, and that is according to the equation:
F=GMm/r^2 , although the value infinity for r can't be added to the equation , but as r approaches infinity F approaches zero.
Even though gravity at infinity equals zero but the expression : F=GMm/(infinity) is not defined.

Redfining simple arithmetic expressions:
It acceptable that:
1+1=2, that is if we have one apple and we put another apple beside it then we will have a total of 2 apples.
4/2=2, that is if we have 4 apples and we want to divide them between two people , then we will give each person 2 apples.

Let's define other expressions with the same logic, these expressions are the subject of speaking:
4/0=0 , we have 4 apples and we want to divide them but we don't have anybody, then we won't divide at all , the process won't occur , in such case the number of apples we divide is zero.The result is zero apples have been divided.

0/0=0, we have nothing to divide and we have no people to divide between , then again the process won't occur at all and while we have nothing , we will divide nothing, and while we have no people then we have no-one to give them anything.The result is zero apples have been divided.

4/(infinity)=0
The same idea we have 4 apples but the number of people is not fixed they change and increases without bound then we can't do the process of dividing, and we can't give any apple to anyone.The process didn't occur and the result is 0 apples have been divided.
Infinity here is not a point or a very large number, infinity is increment in the value of some variable  continuously and without bound.

According to these definition of simple arithmetic expression, we can redfine some equations so that they have meaning:
v=X/t=0/0=0, and that is at the origin when t=0 and x=0
F=GMm/r^2=GMm/(infinity)=0

Relativistic kinetic energy:
K.E=mc²/√(1-v²/c²)-mc²
At the speed v=c for a mass, the expression √(1-v²/c²) will equal zero:
K.E=mc²/0 - mc² ,  K.E = 0-mc²
K.E=-mc²
But energyof mass m equals:
E=mc²
 K.E=-E

The kinetic energy of a mass m moving at the speed of light c equals the energy of the  mass, and that what is the kinetic energy of a photon is, the kinetic energy of a photon is its contained energy, the kinetic energy of a mass m moving at v=c  is its contained energy E , i.e the energy of its mass

The article in vixra:
http://vixra.org/abs/1908.0119

[Bored chemist]

we can redfine some equations so that they have meaning:

They already had meaning.
However, division by zero does not.

[Yahya A.Sharif (OP)]

we can redfine some equations so that they have meaning:

They already had meaning.

They don't, speed equation is a function of the graph x/t that represent all points including t=zero

However, division by zero does not.

It should.

[Bored chemist]

The result is zero apples have been divided.

Which means that you have not done any division.
You can't define "division" to mean "not doing division".

It should.

No.
It should not, because , if you do, you get contradictions.

You really are not going to win this argument after hundreds of years.

[Bored chemist]

speed equation is a function of the graph x/t

Speed has nothing to do with graphs.

[Yahya A.Sharif (OP)]

You can't define "division" to mean "not doing division".

I'm defining " the result of division", division is givining the 4 apples to the two people half for each one"4/2" the result is each one will take two

It should.

No.
It should not, because , if you do, you get contradictions.

What are these contradictions?

You really are not going to win this argument after hundreds of years.

It is like saying Einstein won't win any arguments against Newton.

Speed has nothing to do with graphs.

really? it is only to mention that a graph is a visual represntation of speed equation

[Bored chemist]

Einstein won't win any arguments against Newton.

Einstein had evidence.

I'm defining " the result of division", division is givining the 4 apples to the two people half for each one"4/2" the result is each one will take two

And, your "definition" does not work for division by zero.

What are these contradictions?

[Yahya A.Sharif (OP)]

speed equation is a function of the graph x/t

Speed has nothing to do with graphs.

This only part of what I said, It is meaningless to qoute a part of a full sentence.

Einstein had evidence.o/o=o for speed,and relatistic kinetic energy

I presented evidence too.

It is all about dividing by zero is not possible, I agree
If you think the video has contradictions give me an example that contradict my post to discuss it here

[Kryptid]

Let's define other expressions with the same logic, these expressions are the subject of speaking:
4/0=0 , we have 4 apples and we want to divide them but we don't have anybody, then we won't divide at all , the process won't occur , in such case the number of apples we divide is zero.The result is zero apples have been divided.

Another way of stating division is by making reference to multiplication. Asking "what is four divided by two?" is the mathematical equivalent of asking "what multiplied by two equals four?" In this case, the answer is two. When you try this with zero, it doesn't work. "What is four divided by zero?" is equivalent to "what multiplied by zero equals four?" There is no answer to this question. There is no number you can multiply by zero and get four. So the answer is undefined.

0/0=0, we have nothing to divide and we have no people to divide between , then again the process won't occur at all and while we have nothing , we will divide nothing, and while we have no people then we have no-one to give them anything.The result is zero apples have been divided.

This is undefined as well, but for a different reason. "What is zero divided by zero?" is equal to "what multiplied by zero equals zero?" The answer can be any number at all. Any number multiplied by zero is zero, so you don't have any one answer. That's why this is also undefined.

4/(infinity)=0
The same idea we have 4 apples but the number of people is not fixed they change and increases without bound then we can't do the process of dividing, and we can't give any apple to anyone.The process didn't occur and the result is 0 apples have been divided.
Infinity here is not a point or a very large number, infinity is increment in the value of some variable  continuously and without bound.

What multiplied by infinity equals four? That question also has no answer, so it's undefined.

[Yahya A.Sharif (OP)]

Let's define other expressions with the same logic, these expressions are the subject of speaking:
4/0=0 , we have 4 apples and we want to divide them but we don't have anybody, then we won't divide at all , the process won't occur , in such case the number of apples we divide is zero.The result is zero apples have been divided.

Another way of stating division is by making reference to multiplication. Asking "what is four divided by two?" is the mathematical equivalent of asking "what multiplied by two equals four?" In this case, the answer is two. When you try this with zero, it doesn't work. "What is four divided by zero?" is equivalent to "what multiplied by zero equals four?" There is no answer to this question. There is no number you can multiply by zero and get four. So the answer is undefined.

0/0=0, we have nothing to divide and we have no people to divide between , then again the process won't occur at all and while we have nothing , we will divide nothing, and while we have no people then we have no-one to give them anything.The result is zero apples have been divided.

This is undefined as well, but for a different reason. "What is zero divided by zero?" is equal to "what multiplied by zero equals zero?" The answer can be any number at all. Any number multiplied by zero is zero, so you don't have any one answer. That's why this is also undefined.

4/(infinity)=0
The same idea we have 4 apples but the number of people is not fixed they change and increases without bound then we can't do the process of dividing, and we can't give any apple to anyone.The process didn't occur and the result is 0 apples have been divided.
Infinity here is not a point or a very large number, infinity is increment in the value of some variable  continuously and without bound.

What multiplied by infinity equals four? That question also has no answer, so it's undefined.

For other numbers division and multiplication occured .For dividing by zero it didn't occur, so we can't compare the two. but both have a result
Division didn't occur and that resulted in zero.
Division and non-division are not the same, but division resulted in non-division and non-division resulted in zero , so division resulted in zero

[Yahya A.Sharif (OP)]

Einstein had evidence.

I presented evidence too.  0/0=0 for speed ,gravity equation  and the relativistic kinetic energy equation

[Kryptid]

For other numbers division and multiplication occured .For dividing by zero it didn't occur, so we can't compare the two.
Division didn't occur and that resulted in zero.
Division and non-division are not the same, but division resulted in non-division and non-division resulted in zero , so division resulted in zero

If the division never happened, then you never got an answer. Which is the same as saying that it is undefined.

[Yahya A.Sharif (OP)]

For other numbers division and multiplication occured .For dividing by zero it didn't occur, so we can't compare the two.
Division didn't occur and that resulted in zero.
Division and non-division are not the same, but division resulted in non-division and non-division resulted in zero , so division resulted in zero

If the division never happened, then you never got an answer. Which is the same as saying that it is undefined.

This y/z=x/0 has no meaning, since there is division in the left which occered and definition in the right which didn't, we can't compare the two with equality sign.
but this has a meaning:
V=x/t=0/0, since we have a vairable in the left we want to know its value , V equals the result of the non-division

[Kryptid]

V equals the result of the non-division

Then V is undefined. Non-division can't give you an answer, because it isn't a mathematical operation.

[Yahya A.Sharif (OP)]

V equals the result of the non-division

Then V is undefined. Non-division can't give you an answer, because it isn't a mathematical operation.

It was not a mathematical operation before, but I now add it to mathematical operations, which works for undefined cases.
x/0  , x/∞, 0/0, etc are unique cases in which the operation on them is applied to any variable .
I presented evidence of three equation examples, which turn out to satisfy .

[Kryptid]

It was not a mathematical operation before, but I now add it to mathematical operations, which works for undefined cases.

It doesn't work. It is literally a lack of a mathematical operation.

I presented evidence of three equation examples

They don't give an answer because you didn't actually do anything at all. You can't get an answer by not doing anything. That's like trying to get a result from a computer program by not running the program. By definition, you don't get a result.

which turn out to satisfy .

No it doesn't. It gives the wrong answer. Zero multiplied by zero does not equal four.

[evan_au]

They already had meaning. However, division by zero does not.

I beg to differ with some of my esteemed colleagues; I think that the case of 0/0 is very important in many areas of maths and physics.
- But you can't say what the answer is without more information.
- The process of mathematics (mostly) gives you that information.

Differentiation may be used to calculate the velocity of an object falling under gravity.
- Technically, differentiation is a limit of Δy/Δx as Δx & Δy approach 0
- Differentiating (when it works) is effectively the result when Δy=Δx=0
- If you have an equation for this motion (eg s=½gt²), then the equation provides the necessary additional information (provided the equation meets certain criteria such as smoothness and lack of infinities at this location).
- Differentiating, you have v=gt, which is effectively the result when Δs=Δt=0
- Differentiation is a basic function in maths & physics, and it (mostly) works well, provided you are a bit careful

Let's take another example, which is applicable to your cellphone:
- If you generate a signal with a spectrum of sin(f)/f, it has some nice properties about not interfering with other signals at f=±π, ±2π, ±3π, etc
- But what is the amplitude at f=0? sin(f)/f= 0/0, so you need some more information.
- In this case, the additional information can be provided by L'Hopital's rule:
- If you differentiate the top and bottom, the answer remains the same
- At f=0, sin(f)/f = 0/0 = cos(f)/1 = 1/1=1

0/0=0....The result is zero apples have been divided.

The OP gave the wrong answer in this case, because he did not provide (or have access to) the necessary additional information.

If we take another case: sin(2f)/f at f=0, it also looks like 0/0.
However, when you differentiate at f=0, you get sin(2f)/f=0/0=2cos(2f)/1=2/1 = 2
The answer is different because the additional information in the equation showed it was different.

See: https://en.wikipedia.org/wiki/L%27H%C3%B4pital%27s_rule

Edit: The π was half-baked...

[Yahya A.Sharif (OP)]

They already had meaning. However, division by zero does not.

I beg to differ with some of my esteemed colleagues; I think that the case of 0/0 is very important in many areas of maths and physics.
- But you can't say what the answer is without more information.
- The process of mathematics (mostly) gives you that information.

Differentiation may be used to calculate the velocity of an object falling under gravity.
- Technically, differentiation is a limit of Δy/Δx as Δx & Δy approach 0
- Differentiating (when it works) is effectively the result when Δy=Δx=0
- If you have an equation for this motion (eg s=½gt²), then the equation provides the necessary additional information (provided the equation meets certain criteria such as smoothness and lack of infinities at this location).
- Differentiating, you have v=gt, which is effectively the result when Δs=Δt=0
- Differentiation is a basic function in maths & physics, and it (mostly) works well, provided you are a bit careful

Let's take another example, which is applicable to your cellphone:
- If you generate a signal with a spectrum of sin(f)/f, it has some nice properties about not interfering with other signals at f=±1, ±2, ±3, etc
- But what is the amplitude at f=0? sin(f)/f= 0/0, so you need some more information.
- In this case, the additional information can be provided by L'Hopital's rule:
- If you differentiate the top and bottom, the answer remains the same
- At f=0, sin(f)/f = 0/0 = cos(f)/1 = 1/1=1

0/0=0....The result is zero apples have been divided.

The OP gave the wrong answer in this case, because he did not provide (or have access to) the necessary additional information.

If we take another case: sin(2f)/f at f=0, it also looks like 0/0.
However, when you differentiate at f=0, you get sin(2f)/f=0/0=2cos(2f)/1=2/1 = 2
The answer is different because the additional information in the equation showed it was different.

See: https://en.wikipedia.org/wiki/L%27H%C3%B4pital%27s_rule

Excellent reply.Thanks

[evan_au]

I would also like to add that I think that the case of ∞*0 is also very important in many areas of maths and physics.
- But you can't say what the answer is without more information.
- The process of mathematics (mostly) gives you that information.

Integration may be used to calculate the distance that an object has fallen under gravity.
- Technically, integration divides the x-axis into n small segments of width Δx
- Integration is a limit of nΣy(x)*Δx as n approaches ∞
- Integration (when it works) is effectively the result when n=∞ and Δx=0
- If you have an equation for motion (eg v=gt), then the equation provides the necessary additional information (provided the equation meets certain criteria such as smoothness and lack of infinities at this location).
- Integration is a basic function in maths & physics, and it (mostly) works well, provided you are a bit careful

[Yahya A.Sharif (OP)]

Evan it came to my mind something:
Actually limits are not included in my assumption , Limit of 1/x² as x approaches zero doesn't mean it will actually reach zero in x values , so when I say 1/0=0 I'm not taking about the value of the graph of 1/x² at x=0 ,I'm talking about the value of the arithmetic expression 1/0 .The graph doesn't end up in a a value of y=1/0 "zero is undefined" the graph behaves differently.