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Sagar191980

Fundamental Theory Of Existence.

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When we divide a number other than zero with 1 we get the same number. Dividing with 1 means cutting the number into 1 part, it means the number remains as a single part, the number remains same. When we divide a number with 2 we mean to say that we are cutting the number into 2 parts and we get two halves of the original number. Dividing with zero/0 means we are cutting the number into zero parts or we can say that we are making that number into zero. It means the number has to become zero. It means the number will be equal to zero which is not possible. There is an exception and that number is zero itself. Zero can be divided by zero as we get the same equality. Zero is equal to zero and zero can be cut into zero parts, it means we have the same number without any inequality. Zero can not divide any other number as inequality exists between other numbers and zero.

Division with zero means converting numerator into zero parts. Zero divided by zero is zero as numerator can be converted to zero parts. To divide any number other than zero into zero parts is not possible. For example 1 can not be divided into zero parts. If 1 can be converted into zero parts then we get 1 is equal to zero which is not possible. If 1 can be divided into zero parts we get 1=0 and it means failure of balance, failure of all equations and also failure of all laws that govern existence. 1 is not equal to zero so 1 can not be destroyed into 0 parts and 1 can not be created from 0. It is clear that creation and destruction between 1 and 0 are impossible. 1 can not be created from 0 and 1 can not be destroyed into zero.

1. Any number other than zero can not be divided by zero.

2. Creation is impossible. Also destruction is impossible.

As numerator other than zero can not be cut into zero parts, numerator can not be destroyed into zero parts. And, as numerator other than zero can not be divided into zero parts, inequal numbers can never become equal. If number other than zero can be cut into zero parts by zero then we get equality between inequal numbers. Because if numerator 1 or 2 or 3 or 4 can become zero after cuttting them with 0 then we get 1 = 2 = 3 = 4 = 0 which is impossible. So, creation is also impossible. As inequal numbers can never be equal creation and destruction are impossible. An artist can create and or destroy a piece of art and it is relative creation and relative destruction which are related to change of form. But, absolute creation and absolute destruction are impossible. Absolute creation means 1/2/3/4 apple(s) or 1/2/3/4 mango(s) or 1/2/3/4 lime(s) or 1/2/3/4 orange(s) or 1/2/3/4 kg gold can be created from zero and absolute destruction means something that exists can be converted into zero and we are not talking about change of form. We are talking about appearing from zero and disappearing into zero without change of form which is impossible. If creation + destruction are possible then we get 1 = 2 = 3 = 4 =0. It means 1 can become zero and zero can become 1 also 2 can become zero and zero can become 2 also 100 can become 2000 and 3000 can become million. Which is impossible. Therefore absolute creation and absolute destruction are impossible.

Creation is impossible and it means that Universe can not be created and was never created. It means Universe has beginning for its existence. Also destruction is impossible and it means that Universe has no end.

3. Universe has no beginning and also there is no end to the existence of the Universe.

As creation is impossible, Universe can not increase in quantity and everything in the Universe is finite. So Universe is finite and anything that has physical existence can never increase beyond finite value. Therefore existence of anything physical can never become unlimited or infinite.

4. Existence of anything physical can not be infinite.

As creation and destruction are impossible and as Universe has no beginning and no end too, there is no room for Creator, it means that there is no God in the Universe.

5. God(s) can not exist.

Sir Issac Newton said that Space is absolute and the great Albert Einstein said that space is relative. Albert Einstein said that space can contract and expand under the influence of gravity. Albert Einstein in his ” Theory of relativity said that velocity of light is constant “. And again Albert Einstein came up with a new theory known as General theory of relativity. And, in General theory of relativity Albert Einstein said that gravity bends space and light travelling in a bent space cases light not to escape black holes. He made two mistakes. His first mistake is to conclude that velocity of light is constant and then he explained his postulate with another theory and said that gravity bends space and this is his second mistake. 

In the beginning there was a train experiment concerning velocity of light. What is it? If I am standing on ground without moving and a passenger in train is moving away from me travelling in train then he can look at me as if he is not moving and I am moving away from him. This is called relative movement. And if I am not standing still and if I am walking away from him then he will see me walking away with the speed of train plus with my speed of walking. But, Scientists observed that velocity of light on ground was found to be 186,282 miles per second (299,792 kilometers per second) also if you are the passenger in the moving train and if I am carrying source of light and if you measure velocity of light coming from light source I am carrying then Scientists found out that the velocity of light was found to be same and it is 186,282 miles per second (299,792 kilometers per second) on Earth. Then someone said that there is a substance in Universe called Ether and light travels relative to ether and that is why velocity of light was not found to be relative and it was found to be constant. Several years later two Scientists conducted an experiment and that experiment is known by their names and it is known as Michelson–Morley experiment, after this experiment the two Scientists concluded that there is no such thing as ether. Why is velocity of light is found to be constant and what did the experiment reveal? In the train experiment you must notice that I was carrying light source or source of light and when light is generated from the source it was not being carried by me. Even if the source of light is being carried by a train, you must know that light generated is not being carried by the train and that is why velocity of light is not found to be alterted. This means concluding that this experiment has anything to do with velocity of light being constant or relative is invalid. In Michelson–Morley experiment velocity of light was measured where they did not change gravity. Entire Michelson–Morley experiment was conducted where the gravity is same. For physical objects that are not light or not other forms of electromagnetic radiation gravity is directly proportional to mass. It means 1 kg gold will have less gravitational pull than 2 kg gold. So for gold gravity is directly proportional to mass. But, light is a form of energy and light has both mass and energy. The famous equation E equals to mass times square of velocity of light ( E = m . C square ) says that Mass-energy equivalence states that mass is concentrated energy. The equation says that mass can be converted into energy. This equation is not only equation for Mass-energy equivalence, it also the equation of light. This equation which is also the equation of light says that light is a form of energy with mass and when we consider the relationship of light with gravity we must understand that light is a form of energy with mass. So light’s mass is inversely proportional to gravity as light has both energy and mass. Gold has mass and its mass is directly proportional to gravity and light has both energy and mass and light’s mass is inversely proportional to gravity. Therefore velocity of light is found to be 186,282 miles per second (299,792 kilometers per second) on Earth whereever the gravity value does not change. Velocity of gold was found to be relative even on Earth’s surface. But, velocity of light was found to be of same value on Earth’s surface as light is unlike gold and has inverse relation to mass-gravity. So, gold’s velocity is found to be relative even when there is no change in gravity. But, velocity of light is found to be relative when there is change in gravity. So velocity of light increases on moon than on earth as light’s velocity is inversely proportional to gravity. Moon has lesser gravity than Earth and that is why velocity of light will be more on Moon than on Earth. Therefore gravity bending space in not true and velocity of light is not constant. Space is absolute and velocity of light is relative. Gravity does not bend space. Gravity bends light. Also in computer screen we can have single dimension, two dimensions and three dimensions. In computers single dimension is line, two dimensional object is square and also in computers three dimensional object is cube. So, in virtual reality we can have single, double and triple dimensions. In physical world or universe the fundamental object like atom itself are three dimensional and in physical world less than 3 and more 3 dimensions are not possible. So, string theory which claims more than 3 physical dimensions is not correct in physical existence. Single dimension is associted to length, double dimension to area and triple dimension to volume. If string theory is correct and there are more than 3 space dimensions then we must have more than volume, which is clearly not observed to be true.

6. Velocity of light is relative.

7. Space is absolute. Space is three and three dimensional only.

Also time is a representation of change and in a changing universe there is no going back or going forward as there are no unlimited universes with unlimited changes. Time travel is not only impossible but does not make any sense. There is only our world or universe and it is chaning and there is no going back in time and also no going forward in time. Existence is finite and time travel is meaningless.

8. Time travel is impossible.

Edited by Strange
Reduced font size to something readable

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!

Moderator Note

Moved to Speculations. Please not the rules for this section of the forum: in particular the need to provide support for your claims.

 
5 minutes ago, Sagar191980 said:

1. Any number other than zero can not be divided by zero.

Zero cannot be divided by zero either.

5 minutes ago, Sagar191980 said:

2. Creation is impossible. Also destruction is impossible.

Define what you mean by "creation" and "destruction".

For example, we know that atoms larger than hydrogen are created in stars.

And we now that, for example, matter and antimatter will destroy each other (and create photons).

So your claim appears to be false.

7 minutes ago, Sagar191980 said:

3. Universe has no beginning and also there is no end to the existence of the Universe.

Do you have any evidence for this?

7 minutes ago, Sagar191980 said:

4. Existence of anything physical can not be infinite.

Do you have any evidence for this?

8 minutes ago, Sagar191980 said:

6. Velocity of light is relative.

This is shown to be wrong by the evidence.

8 minutes ago, Sagar191980 said:

7. Space is absolute.

This is also shown to be wrong by the evidence.

8 minutes ago, Sagar191980 said:

8. Time travel is impossible.

Do you have any evidence for this?

 

You have made a series of claims with no evidence. Several of them are know to be wrong. Is there any reason to keep this thread open?

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First quote reply: Zero can divide zero. How? Because division by zero means numerator becomes zero and it should equal to zero. As zero is equal to zero. We have a perfect equation.

Second quote reply: I posted that change related creation and change related destruction are possible. They are relative creation and relative destruction.

Third quote reply: Absolute creation and absolute destruction are not possible. Hence true.

Fourth quote reply: As absolute creation is not possible, finite Universe can never become infinite. 

Fifth quote reply: Velocity of light is relative and light's velocity has to be measured in lower or higher gravity fields than that of Earth's measured velocity of light. The provided evidence is flawed and I gave an explanation why it is flawed.

Sixth quote reply: Gravity controls light, gravity doesn't control space. The evidence provided is flawed. The truth is Albert Einstein proposed that velocity of light is constant and then he supported his claim with another flaw.

Seventh quote reply: Time travel is not possible. The Universe that exists changes and there is no existence of past change and time travel to past is thus meaningless also future change is not a seperate existence, present existence changes with time and new past is created. So, future time travel is meaningless as there is no such existence.

 

I had to post earlier so that the post would not be deleted. And added more to it by editing. Thanks.

Edited by Sagar191980

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2 minutes ago, Sagar191980 said:

Because division by zero means numerator becomes zero and it should equal to zero.

Please provide a reference to support his. It is blatantly false.

3 minutes ago, Sagar191980 said:

Second quote reply: I posted that change related creation and change related destruction are possible. They are relative creation and relative destruction.

This sentence appears to be meaningless. Unless you can define what you mean by "change related creation/destruction" and "relative creation/destruction". 

I gave examples of creation and destruction. So your claim they are impossible appears to be false.

5 minutes ago, Sagar191980 said:

As absolute creation is not possible, finite Universe can never become infinite. 

A finite universe can never become infinite.  An infinite universe has always been infinite.

Now, what evidence do you have that the universe is not finite?

5 minutes ago, Sagar191980 said:

Velocity of light is relative

It is shown to be invariant by both theory and experiment. So this is false.

Quote

The provided evidence is flawed and I gave an explanation why it is flawed.

You "explanation" is incoherent nonsense. You clearly don't know what you are talking about.

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Can we please have one speculation per thread?

If a subject is worth speculating it is worth a thread of its own.

 

Edited by studiot

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9 minutes ago, Sagar191980 said:

First quote reply: Zero can divide zero. How? Because division by zero means numerator becomes zero and it should equal to zero. As zero is equal to zero. We have a perfect equation.

"Dividing by Zero is undefined."

https://www.mathsisfun.com/numbers/dividing-by-zero.html

"In mathematics it is a rule that we cannot divide by zero, because it contradicts the other rules of mathematics."

https://brilliant.org/wiki/division-by-zero/

"In mathematics, division by zero is undefined."

https://study.com/academy/lesson/dividing-by-zero-definition-lesson-quiz.html

More here: http://mathforum.org/dr.math/faq/faq.divideby0.html

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Dividing the numerator with denominator means cutting the numerator using the denominator. 2 divided by 3 means 2 is cut into 3 parts. 2 divided by zero means 2 is cut into zero parts or to say that 2 become zero and then 2 is not equal to zero. Zero can not divide 2 as 2 can not become zero parts. But zero is already zero parts and equality of zero divided by zero equals to zero is also true as zero = zero. Numerator zero cut with denominator zero gives answer zero and it is satisfied as zero equals zero. But, numerator 2 can not divided with denominator zero as 2 can never equal to zero parts. 2 can never become zero parts. As 1 can never become zero and zero can never become 1, 1 can not be cut into zero parts or 1 can not be destroyed into zero parts. Also zero can not become 1 as 1 and zero can never be equals so creation is also not possible.

 

You gave examples of creation and destruction. Those examples are change of form, they are creations from existence. They are not creation from non existence.

Edited by Sagar191980

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Just now, Sagar191980 said:

Dividing the numerator with denominator means cutting the numerator using the denominator. 2 divided by 3 means 2 is cut into 3 parts. 2 divided by zero means 2 is cut into zero parts or to say that 2 become zero and then 2 is not equal to zero. Zero can not divide 2 as 2 can not become zero parts. But zero is already zero parts and equality of zero divided by zero equals to zero is also true as zero = zero. Numerator zero cut with denominator zero gives answer zero and it is satisfied as zero equals zero. But, numerator 2 can not divided with denominator zero as 2 can never equal to zero parts. 2 can never become zero parts. As 1 can never become zero and zero can never become 1, 1 can not be cut into zero parts or 1 can not be destroyed into zero parts. Also zero can not become 1 as 1 and zero can never be equals so creation is also not possible.

Your claims of dividing by zero are false. To keep repeating this is therefore dishonest.

1 minute ago, Sagar191980 said:

You gave examples of creation and destruction. Those examples are change of form, they are creations from non existence.

This is why I asked you to define what you mean by "creation" and "destruction". Why have you not done that?

 

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I explained that 1 can not become zero it means 1 can not be destroyed into zero.

I also typed that zero can not become 1 and it means creation of 1 from zero is not possible.

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4 minutes ago, Sagar191980 said:

I explained that 1 can not become zero it means 1 can not be destroyed into zero.

I also typed that zero can not become 1 and it means creation of 1 from zero is not possible.

Of course not. They are different numbers. It is equally true (and equally irrelevant) to say that 5 cannot become 12.

This has nothing to do with physics or creation/destruction.

 

So, in summary, we have four provably false claims:

Quote

1. Any number other than zero can not be divided by zero.

2. Creation is impossible. Also destruction is impossible.

6. Velocity of light is relative.

7. Space is absolute. 

And four that are unknown and, possibly, unknowable:

Quote

3. Universe has no beginning and also there is no end to the existence of the Universe.

4. Existence of anything physical can not be infinite.

5. God(s) can not exist.

8. Time travel is impossible.

You have provided no evidence to support any of these claims.

So there is no science here and I will request this thread is closed.

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1 minute ago, Sagar191980 said:

In physics if you say creation of something from nothing then it is same as something created from zero.

There is no evidence for anything created from nothing. So why are you claiming there is?

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4 hours ago, Sagar191980 said:

2. Creation is impossible. Also destruction is impossible.

"creation" and "destruction" are man-made humanistic words to describe process in which they gain or lose something. i.e. somebody has wood, and burns it on fire. Destruction for humanist! But from point of view of scientist, it's just reaction between organic matter with Oxygen from air i.e. transformation.

In mathematics, "creation" and "destruction", senseless statements. In physics, we have pair-production, photo-disintegration, and similar effects which are examples of transformations from one particle to other particle(s), from one molecule to other molecule(s). Conservation of physical constants prior and after reaction between molecules, atoms, or particles. i.e. charge must be conserved, energy must be conserved, baryon number must be conserved, lepton number must be conserved etc. etc. Major part of quantum physicist's work is attempt of discovery of violation of some conservation rule, which was established in the past, which would give them fame and Nobel prize...

 

Was the Earth created? Or it's made of matter which used to exist in the past prior 4.5 billion of years.. ?

Was the Sun created? Or it's made of matter which used to exist in the past.. ?

Gas cloud of Hydrogen and Helium collapsed in the center of accretion disk, and made the Sun. No human can go back in time, check it, and return here, and confirm that it's true.

For humanist it's "the Sun has been created". For scientist it's "the Sun has been made of the matter that existed and collapsed due to gravity"..

See the difference? The first statement is making something from nothing. In the second, it's just transformation from one existing thing to other existing thing, during millions or billions of years of cosmic evolution.

 

Edited by Sensei

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10 hours ago, Sensei said:

"creation" and "destruction" are man-made humanistic words to describe process in which they gain or lose something. i.e. somebody has wood, and burns it on fire. Destruction for humanist! But from point of view of scientist, it's just reaction between organic matter with Oxygen from air i.e. transformation.

In mathematics, "creation" and "destruction", senseless statements. In physics, we have pair-production, photo-disintegration, and similar effects which are examples of transformations from one particle to other particle(s), from one molecule to other molecule(s). Conservation of physical constants prior and after reaction between molecules, atoms, or particles. i.e. charge must be conserved, energy must be conserved, baryon number must be conserved, lepton number must be conserved etc. etc. Major part of quantum physicist's work is attempt of discovery of violation of some conservation rule, which was established in the past, which would give them fame and Nobel prize...

 

Was the Earth created? Or it's made of matter which used to exist in the past prior 4.5 billion of years.. ?

Was the Sun created? Or it's made of matter which used to exist in the past.. ?

Gas cloud of Hydrogen and Helium collapsed in the center of accretion disk, and made the Sun. No human can go back in time, check it, and return here, and confirm that it's true.

For humanist it's "the Sun has been created". For scientist it's "the Sun has been made of the matter that existed and collapsed due to gravity"..

See the difference? The first statement is making something from nothing. In the second, it's just transformation from one existing thing to other existing thing, during millions or billions of years of cosmic evolution.

 

What an excellent and positive viewpoint. +1

We should perhaps add to this the issue of the creation / destruction of something abstract.

Creation and destruction are transitive verbs which means they operate on something and require an 'object noun'.
Therefore the OP needs to clearly define the 'object' noun in this case.

Edited by studiot

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11 hours ago, Sensei said:

"creation" and "destruction" are man-made humanistic words to describe process in which they gain or lose something. i.e. somebody has wood, and burns it on fire. Destruction for humanist!

This is a good post, but I would just point out that you are sing "humanist" in a rather non-standard way. I assume you just mean "human" (as an adjective) or something?

26 minutes ago, studiot said:

Creation and destruction are transitive verbs

Sorry: just being picky (again) but they are nouns, and the related verbs can be both transitive and intransitive. 

But I agree with your point that the OP needs to clarify what they mean by these words. I don't think there is any reason to think that something can be created "from nothing" (depending how "nothing" is defined) so I don't know why the OP is expending so much effort on it.

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On 9/22/2019 at 11:44 AM, Sagar191980 said:

As numerator other than zero can not be cut into zero parts, numerator can not be destroyed into zero parts. And, as numerator other than zero can not be divided into zero parts, inequal numbers can never become equal. If number other than zero can be cut into zero parts by zero then we get equality between inequal numbers. Because if numerator 1 or 2 or 3 or 4 can become zero after cuttting them with 0 then we get 1 = 2 = 3 = 4 = 0 which is impossible. So, creation is also impossible. As inequal numbers can never be equal creation and destruction are impossible. An artist can create and or destroy a piece of art and it is relative creation and relative destruction which are related to change of form. But, absolute creation and absolute destruction are impossible. Absolute creation means 1/2/3/4 apple(s) or 1/2/3/4 mango(s) or 1/2/3/4 lime(s) or 1/2/3/4 orange(s) or 1/2/3/4 kg gold can be created from zero and absolute destruction means something that exists can be converted into zero and we are not talking about change of form. We are talking about appearing from zero and disappearing into zero without change of form which is impossible. If creation + destruction are possible then we get 1 = 2 = 3 = 4 =0. It means 1 can become zero and zero can become 1 also 2 can become zero and zero can become 2 also 100 can become 2000 and 3000 can become million. Which is impossible. Therefore absolute creation and absolute destruction are impossible.

I would disagree.  The simplest equation on the coordinate plane is y=kx.  Then k represents your constant of proportionality.  Then every line that crosses the orgin can have the same rate of change or slope by taking any Y on that line and dividing by the corresponding X of that point on the line.  They will all produce the same value for k except the point (0,0).

Then the constant of proportionality can actually be anything at the point (0,0).  At every other point on the coordinate plane the constant of proportionality can only have one single value for every line that crosses through the origin.

It would lead me to the conclusion that 0/0 can actually be any/every value or rate, because every line with a constant of proportionality that is different crosses through that point.

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Posted (edited)
5 hours ago, Conjurer said:

Then k represents your constant of proportionality.  Then every line that crosses the orgin can have the same rate of change or slope by taking any Y on that line and dividing by the corresponding X of that point on the line.  They will all produce the same value for k except the point (0,0).

The slope is defined as the change in the y coordinate divided by the corresponding change in the x coordinate, between two distinct points on the line. 

render.png

In your example you first use (x,y) and implicitly (0,0) which is ok. Then you seem to try to use (0,0) twice and that is not how slope is defined, you need two different points along the line. Here is what you seem to be suggesting, but this is not the definition of slope:

render.png

5 hours ago, Conjurer said:

Then the constant of proportionality can actually be anything at the point (0,0).  At every other point on the coordinate plane the constant of proportionality can only have one single value for every line that crosses through the origin.

No. The constant of proportionality is the same in point (0,0) as in any other point along a specific line through point (0,0). Point (0,0) is not special. 

 

Edited by Ghideon
added missing last part

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Maths is a nightmare to me, but I thought I'd still venture to ask for clarification. 

If you divide something by 3, you get 3 smaller things. If you divide by 2, you get 2 slightly bigger things. If you divide it by 1, you are not dividing it at all. If you divide it by less than one, you are not dividing it, you are multiplying it. Divide it by 0.5, you are ACTUALLY multiplying it by 2. Divide it by O.1, you are really multiplying it by 10.

So divide something real by 0, you are really multiplying it by infinity, and not dividing it at all. So although 0 is a number, infinity is not. So if you write X/0 you are simply trying to express the infinite as something finite. 

That makes 0 a special number, you can multiply real things with it, but you can't divide by it. 

At least, that's how I've always seen it. 

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I was going to start by asking Conjurer why he revived this old thread ?

However there still seems to be interest in it so here  my thoughts.

47 minutes ago, mistermack said:

Maths is a nightmare to me, but I thought I'd still venture to ask for clarification. 

If you divide something by 3, you get 3 smaller things. If you divide by 2, you get 2 slightly bigger things. If you divide it by 1, you are not dividing it at all. If you divide it by less than one, you are not dividing it, you are multiplying it. Divide it by 0.5, you are ACTUALLY multiplying it by 2. Divide it by O.1, you are really multiplying it by 10.

So divide something real by 0, you are really multiplying it by infinity, and not dividing it at all. So although 0 is a number, infinity is not. So if you write X/0 you are simply trying to express the infinite as something finite. 

That makes 0 a special number, you can multiply real things with it, but you can't divide by it. 

At least, that's how I've always seen it. 

 

That about sums up common or garden use of arithmetic. so +1

8 hours ago, Conjurer said:

I would disagree.  The simplest equation on the coordinate plane is y=kx.  Then k represents your constant of proportionality.  Then every line that crosses the orgin can have the same rate of change or slope by taking any Y on that line and dividing by the corresponding X of that point on the line.  They will all produce the same value for k except the point (0,0).

Then the constant of proportionality can actually be anything at the point (0,0).  At every other point on the coordinate plane the constant of proportionality can only have one single value for every line that crosses through the origin.

It would lead me to the conclusion that 0/0 can actually be any/every value or rate, because every line with a constant of proportionality that is different crosses through that point.

This is the first thread I have seen you post that is coherent and rational, even if it is partly flawed.

However you have identified and highlighted the correct part of the OP which is that there is something different about division by zero.

So +1

A small niggle, I would say that the simplest equations in a plane is the line y = k or x = h, where h and k are constants.

The idea of proportionality is good but more restrictive since my two equations do not display proportionality.
However we should always require general statements to cater for the most general case so I will continue with equations.

3 hours ago, Ghideon said:

No. The constant of proportionality is the same in point (0,0) as in any other point along a specific line through point (0,0). Point (0,0) is not special

Ghideon is correct here. The constant of proportionality is well constant, which means it is defined as having only one value.
But as I said, employing it is restrictive.

Employing the slope of a line is even more restrictive and I think both you and Ghideon are wrong to use it.

Particularly as Ghideon's definition does not even include the more general case of y = mx, where the slope at a single point is defined.

 

OK so what to do?

 

Well we are dealing with the arithmetic of numbers and when faced with this situation Mathematicians turn to Set theory.

The numbers come from a particular type of set called a Field.

To qualify as a Field both the set and its elements must prossess certain properties.

Importantly here the set must have at least two separate 'binary operation's defined on it.
These can be defined by equations a + b = c and a * b = d where  a, b, c and d are elements of the set and are commonly called addition and multiplication.
Note there must be at least 2 operations, not  or 1. Some fields have additional operations, but they are not used in arithmetic or required in the definition.

The elements of a Field are all of the same type which means that c and d must be numbers (in our case) of the same type as a and b.

There are several other requirements (to total 9 in all) collectively called the Field axioms,
But the other important one to us is that no number can be missing. This is called closure and the set is a set of all numbers of the type of number we are using.
This will, of course, include zero itself.

So not all sets of numbers are Fields.

 

This curious setup has many advantages which allowing division by zero would take away from us.
But there is already a slight difficulty creeping in.

The advantages are that this setup guarantees that every equation of the sort a + b = c and a * b = d will have a solution, with one exception.
And also that whenever we perform these binary operations, we will always get a number and nothing but a number. and further we can do this for each and every pairing of numbers.

The exception is that there is no solution to equations of the type 0 * a = 9.

This is resolved by disallowing division by zero. The phrase division by zero is not defined.
A small price to pay for the univesality and usefulness of the normal system of arithmetic.

Three further notes.

Firstly the smallest field is the field with just two numbers, 0 and 1.

It is mathematically possible to define a mathematical structure (called an extended field) by adding special elements which will allow division by zero.
But the price is that the extra elements are not numbers and we cannot guarantee what we will get if we use our equations.

Finally division by zero and the fraction 0/0 are different and require different handling.

 

 

 

 

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6 hours ago, studiot said:

The numbers come from a particular type of set called a Field.
...

Thank, helpful introduction inspiring to some more reading! I do not remember studying of that part of mathematics in any depth. 

 

6 hours ago, studiot said:

Employing the slope of a line is even more restrictive and I think both you and Ghideon are wrong to use it.

Particularly as Ghideon's definition does not even include the more general case of y = mx, where the slope at a single point is defined.

Probably wasn't clear in that post, in my line of thought I did not realise a more general case was needed to make a point. Maybe you can you elaborate where I went wrong? I'm aware of slope being defined at a single point*. I intended to comment on the calculation using a single point. Example; given the question "A straight line goes through point (0,0), please calculate the slope" I would need one more point along the line to give an answer?  

 

 

*) Slightly of topic but worth mentioning; vocabulary may not be same in all languages, possibly confusion my posts. Over here "k" is normally only used for slope of straight lines and m used for the constant in y=kx+m. 

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2 hours ago, Ghideon said:

*) Slightly of topic but worth mentioning; vocabulary may not be same in all languages, possibly confusion my posts. Over here "k" is normally only used for slope of straight lines and m used for the constant in y=kx+m.

There is somewhat a measure of fashion about what symbols are used for what purpose.

In most english language texts on coordinate geometry a straight line has the equation y = mx +c.

2 hours ago, Ghideon said:

Probably wasn't clear in that post, in my line of thought I did not realise a more general case was needed to make a point. Maybe you can you elaborate where I went wrong? I'm aware of slope being defined at a single point*. I intended to comment on the calculation using a single point. Example; given the question "A straight line goes through point (0,0), please calculate the slope" I would need one more point along the line to give an answer?

You are not entirely wrong.

It's just that you were using two points.

A mathematician would be perfectly happy with the answer "the slope is m." ,

since any value of m will suffice.

Or if m has been specified (say 0.5) the the slope is 0.5.

Naturally c would also need to be specified - in this case the statement goes through the point (0,0) is sufficient to identify it as equal to zero.

The equation


[math]m = \frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}[/math]


is just one of many derived forms, and the definitions need to encompass all of them.

Here is a short list

strtlin1.jpg.84638e8e64adc6608744bfcf3e8cfcd9.jpg

 

As a matter of interest I included that stuff about the field {1,0}

because it is discrete and of tremendous use in truth tables and computing mathematics.

Fields have many other use for instance they are part of the basc definition of a mathematical vector and vector space axioms.

 

So abandoning them to allow division by zero would have unwanted rippled throughout applied maths.

 

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2 hours ago, studiot said:

 

In most english language texts on coordinate geometry a straight line has the equation y = mx +c.

 

 

Lol I'm more used to y=mx+b but that's trivial  lol.

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