The two types of Zero

[Revoltingest]

Look, you can do what you want, but I'll keep using Zero Undefined because it makes sense to me to use it over using Null. To me, I see Null as being something to be used within programming, and Zero Undefined I understand to be used outside of programming, to be Null's equivalent outside of programming. If I say I'm using Null, it would mean that I'm doing something with programming, but if I say I'm using Zero Undefined it means I'm doing something outside of programming.

You need rigorous definitions of your kinds
of zero. That would make discussion easier.

 

[wellwisher]

Zero defines nothing by definition. If I have zero money in my pocket, there is not money in my pocket. You can look, you will see no money. If I do not let you look, I can claim I have a lots of money in my pocket but this will not be provable. The question is what can you do with nothing, in math?

One way to approach this question is to first look at division by small numbers such as fractions. As an example, consider the miracle of Jesus when he fed a multitude of thousands with just one fish and one loaf of bread. One way he could to feed the crowd, would be to divide the one fish and one bread by 1/2000, so he can get 2000 fish and 2000 loaves of bread. Division by a faction, which we do all the time, gives math proof to this miracle.

Say Jesus wanted to really show off and instead of divided by 1/2000, he divided the one fish and one bread by 0. He would have infinite fish and infinite bread, which is more organic material, than was in the entire solar system at that time. This would violate conservation principles and therefore would not be possible in space-time, under the current laws of physics. That would be a miracle of miracles; able to violate conservation. Math does this all the time, so what is the physical basis for this division by less than one; to zero, operation?

If I have one apple and divide it by two, I still have one apple but in two pieces. This satisfies conservation and does not need sleight of hand magic to do. All I need is a sharp knife and skilled hand/eye. But if I divide the apple by 1/2, I get two apples. How is that physically possible? This example, could be done with a magic sleight of hand trick; extra apple up my sleeve. But how can we materialize an extra apple without magic. Would division by 1/2 need futuristic technology that can assemble an apple from the hidden quantum world?

If we divide the apple by zero, holy crap that is a lot of apples and even the up the sleeve magic trick would be stumped. Does division by fractions and zero have any space-time explanation? Does this operation follows the laws of physics, or does it follow other laws beyond the known laws of physics? Or it this just imaginary or some form of magic trick?

In Einstein theory of Special Relativity, the multiplier is 1/(1-v2/c2), where v is velocity and c is speed of light. As velocity v increases 1/(1-v2/c2) becomes a fraction less than one, and starts to multiply distance, time and mass. Interestingly, in this case, division by a fraction has been proven with this equation, with time slowing down in experiments of radioactive decay in particle accelerators; decay rate actually slows.

This is quite strange, in that it actually works for these reference variables, including mass, but not for apples. Technically, the mass does not change, since mass is an invariant. Rather another deeper as aspect of mass; its relativistic mass, increases. The particle behaves like it got heavier, by since mass is invariant no extra mass is added, but the effect is like it did; weird. It appears the old timers of math saw a future where this operation, that appears to violate space-time based conservation, could produce a valid result in physics.

My interpretation is division by fractions, all the way to zero, is less connected to material or space-time reality, including rest mass, which exist in space-time, but rather is connected to where material reality in space-time intersects where space and time are not connected and each can act as an independent variables. This is the basis for consciousness; human imagination and the quantum world.

The human brain can generate imaginatary scenarios that can violate the limits of space-time. This is not happening in space-time reality; fiction, but is based on the organizing of information into a book of fiction. The brain can process information, which is based on space-time reality processing, but in ways the output information is shuffled, to form new organization, not fully representative of reality.

For example, say I randomly change the order of the words in the last sentence. New meaning or gibberish would result that may not represent part of reality or may suggest a different part. This constructive shuffle of information is connected to consciousness; I think therefore I am. I can exceed the law of space-time in terms of informational representations; science fiction. This shuffle also brings to the quantum world, where the speed of light can be violated; outside space-time.

Relativistic mass is altering the properties of the invariant mass, goes beyond space-time, via an interaction with separated space and time. There is potential added, but not based on conservation principles in space-time; shuffle.

In math, we do worry about conservation when dealing with division by fractions; divide a gallon go gasoline by 1/2 to get 2. However, it was define in as such a way; allowable operation, without trying to equate the operation to only space-time reality. It appears the Old Timers of Math were initiative of something more, but not yet tangible, where this all adds up, when we do the math. It was view to the other side, since division by fractions and zero is not about this side of reality, at least all by itself.

 

[Polymath257]

Some of your claims are not quite correct.

In Einstein theory of Special Relativity, the multiplier is 1/(1-v2/c2), where v is velocity and c is speed of light.

Close, but not quite right. The correct multiplier is the square root of this quantity.

As velocity v increases 1/(1-v2/c2) becomes a fraction less than one, and starts to multiply distance, time and mass.

Um, no. As v increases, 1-v^2/c^2 *decreases* so 1/sqrt(1-v^2/c^2) *increases* and is *more* than one. This is the factor that (apparent) mass gets multiplied by. But time intervals and length get multiplied by sqrt(1-v^2/c^2). So moving lengths appear *shorter* as do time intervals (slower clocks).

It is also important that this effect goes *both ways*. If You are moving past be at a velocity of v, then I am moving past you with a velocity of v in the opposite direction. That means that *both* of us see the clocks of the other as being slower, lengths as being shorter and masses as being larger.

Interestingly, in this case, division by a fraction has been proven with this equation, with time slowing down in experiments of radioactive decay in particle accelerators; decay rate actually slows.

Yes.

This is quite strange, in that it actually works for these reference variables, including mass, but not for apples. Technically, the mass does not change, since mass is an invariant. Rather another deeper as aspect of mass; its relativistic mass, increases. The particle behaves like it got heavier, by since mass is invariant no extra mass is added, but the effect is like it did; weird. It appears the old timers of math saw a future where this operation, that appears to violate space-time based conservation, could produce a valid result in physics.

The relativistic mass is relevant though, in interactions. For example, if you collide two protons that are moving close to the speed of light with respect to each other, the result may well have a *rest* mass much more than the rest masses of the two protons. In fact, it is possible (and even common in some accelerators) to get multiple protons and anti-protons out of such a collision.

 

[Ponder This]

I have realized that there are two types of zero in Math, and both are important to understand. Here they are:

A. Divisible Zero: This version of zero would function within the conventional mathematical framework, where zero is treated as a numerical value that can participate in arithmetic operations. For example, in standard mathematics, zero divided by any non-zero number is zero, and this rule would apply to 'divisible zero'. This concept aligns with the traditional understanding of zero in mathematics.

B. Zero Undefined: This type of zero would represent a concept that is not just the absence of quantity, but an absence of definable or divisible substance. It's a conceptual placeholder for something that is fundamentally indeterminate or unquantifiable. In this context, dividing 'zero undefined' would not make sense, as it represents a state or condition that is beyond the scope of standard arithmetic operations.

Allow me to give you an example as to why these two zero types are important. Say you have a basket of 3 oranges and 1 apple. When counting how many oranges you have, the apple would be a 0 in the equation, but it would be a divisible zero because you understand that if you divide the apple in half, you will get two slices, but it would still be zero oranges. But let's say in that basket there were only known to be 3 oranges. In this case zero would be Zero Undefined because the absence of oranges in the basket couldn't be said to be the amount of space remaining in the basket because it was never said there was nothing else in the basket, it was only said there were 3 oranges, therefore you cannot divide that type of zero in half because it hasn't been defined enough.

(Right here I deleted something about 0/0 because I realized I had made a mistake. However, the rest of everything is correct. Still, I would like to clarify that I've realized Zero Undefined is more useful for philosophy than mathematics.)


+++

Edit: For those of you who still think that Zero undefined is still a useless word, I will explain to you their non-math uses via different words:

First word, Non-Applicable Existence (noun) (Equal to Divisible Zero):

Definition: An existence that is not relevant or applicable to a particular context or situation.
Example usage: "In the context of the experiment, the scientists determined that certain entities were non-applicable existences and therefore removed them from the experimental conditions."

Etymology: "Non-" meaning "not" or "without," and "applicable" meaning "relevant or appropriate to a particular situation."

This term is used to emphasize the presence of an entity or phenomenon while also acknowledging its lack of relevance or applicability to a particular context or situation. It is often used in scientific or technical contexts and can help to make more precise and accurate predictions or decisions by distinguishing between entities that are relevant and those that are not relevant to a given context.

More detailed explanation: "Non-applicable existence" refers to the existence of something that is not relevant or applicable to a particular context or situation. It is a way of categorizing and understanding the presence of something in relation to a specific set of circumstances or conditions.

For example, in a scientific experiment, certain entities or phenomena may be considered "non-applicable existences" if they do not have a direct impact on the outcome of the experiment. While they may still have some level of existence or presence, they are not relevant or applicable to the specific conditions of the experiment and can be ignored or removed without affecting the results.
The term "non-applicable existence" can be used in technical or scientific contexts to make more precise and accurate predictions or decisions by distinguishing between entities that are relevant and those that are not relevant to a given context. It is a way of acknowledging the presence of something while also explaining its relationship to other entities or phenomena.

+++

Second word, Less Than Non-Applicable Existence (noun) (Equal to Zero Undefined):
Definition: A hypothetical state of existence that is so insignificant and irrelevant to a particular context or situation that it cannot be distinguished from not being there at all. It denotes a level of existence that is so minimal that it has no practical or observable impact on the world or any system.

As a purely hypothetical concept, "less than non-applicable existence" does not have any concrete existence in the physical world, and it is difficult to conceive of it in any tangible way. However, from a logical standpoint, it is possible to imagine a state of existence that is so insignificant or irrelevant to a particular context that it might be considered "less than non-applicable."

For example, consider a hypothetical scenario where a scientist is conducting an experiment to measure the effects of a particular substance on the growth of plants. In this context, the plants are the primary focus of the experiment, and any other entities present in the environment, such as microbes or insects, may be considered "non-applicable existences" since they are not directly relevant to the outcome of the experiment.

However, if there were even smaller entities or particles present in the environment that had such little impact on the experiment that they were effectively indistinguishable from not being there at all, they might be considered "less than non-applicable existences."
From a logical perspective, the concept of "less than non-applicable existence" is possible because it is simply a way of describing a degree of existence or presence that is so minimal or insignificant that it is effectively negligible. While it may not have any concrete manifestation in the physical world, the concept is not inherently contradictory to logic or reason.

More detailed explanation: Try thinking about it this way, there could be an object that you will never think about, but that doesn't mean that object that you will never think about isn't a real thing, it just means that you'll never think about it.

This is a great realization for you to have: that there are different ways of thinking about nothing or void or null or zero.
Some more thoughts and tell me what you think of these...

• a system of equations with no solution. This is a form of nothing that is not zero. In fact, 0 could be the solution to a system of equations. But for a system of equations to have no solution, it can't even have 0 as a solution.
• N/A, is an abbreviation for "not available", "not applicable", "not assessed", or "no answer" Given your description of non-applicable existence, I think you might be interested in the use of the N/A abbreviation.
• there also exist word problems for which no solution exists because insufficient information was given to solve the problem. In such as case, additional information might result in infinitely many solutions, a finite number of solutions, or even no solution. This lack of information is a kind of nothing.
• In mathematics, we have vectors in n-dimensions or even infintely many dimensions. If the first dimension was oranges and the second dimension was apples, then we might make a vector (3, 1) repesenting 3 oranges and 1 apple. Of course, such a vector would exist in a two-dimensional space we can imagine is contained in a larger dimensional space. Perhaps some vector (3, 0, ...), where the elipsis represent the rest of the larger dimensional space. An elipsis represents an omission. What sort of nothing is that, do you think?

Anyway, I appreciate your musings on the nature of nothing as there is quite a lot of nothing to muse on.

 

[Heyo]

This is a great realization for you to have: that there are different ways of thinking about nothing or void or null or zero.
Some more thoughts and tell me what you think of these...

• a system of equations with no solution. This is a form of nothing that is not zero. In fact, 0 could be the solution to a system of equations. But for a system of equations to have no solution, it can't even have 0 as a solution.

Fyi, in maths, no solution is written {}, the empty set.

 

[Polymath257]

They’re a nice book on the medieval thoughts on the vacuum called “Much Ado About Nothing”.

Off you want to read some interesting philosophy and its history, check it out.

No, not the Shakespeare play.

 

[wellwisher]

Some of your claims are not quite correct.

Close, but not quite right. The correct multiplier is the square root of this quantity.

Um, no. As v increases, 1-v^2/c^2 *decreases* so 1/sqrt(1-v^2/c^2) *increases* and is *more* than one. This is the factor that (apparent) mass gets multiplied by. But time intervals and length get multiplied by sqrt(1-v^2/c^2). So moving lengths appear *shorter* as do time intervals (slower clocks).

It is also important that this effect goes *both ways*. If You are moving past be at a velocity of v, then I am moving past you with a velocity of v in the opposite direction. That means that *both* of us see the clocks of the other as being slower, lengths as being shorter and masses as being larger.


Yes.

The relativistic mass is relevant though, in interactions. For example, if you collide two protons that are moving close to the speed of light with respect to each other, the result may well have a *rest* mass much more than the rest masses of the two protons. In fact, it is possible (and even common in some accelerators) to get multiple protons and anti-protons out of such a collision.

Above I was trying to do this from memory and forgot the extra square root.

In the twin paradox, one twin is stationary and the other twin leaves the earth, on a spaceship, that requires fuel conversion to propulsion, to gain the kinetic energy for the ship, so the ship can reach the needed relativistic velocity.

Although both references may appear to see each other the same way; relative reference, one reference is an illusion reference, since both references did not use energy to gain genuine relativistic changes. E=MC2 equates the relativistic mass change to the fuel energy conversion to kinetic energy. This is imaginary energy in the stationary relative earth reference. Only the moving twin ages since he had genuine energy needed for relativistic mass and time dilation; age slower. He may have expected to see his brother the same age, due to relative reference, but he saw an old man, since his brother did not have real energy based SR time dilation.

When experiments were done, with radioactive decay in particle accelerators, the radioactive particles were supplied magnetic energy for conversion into kinetic energy, from an electric power source; got an electric bill. If we were sitting on these particles, we may appear to see the lab move, but that would be an illusion due to our own relativistic energy.

This application of energy conservation to Special Relativity; I used to mention this years ago, caused some in physics to want to play down relativistic mass, so they can assume only relative references and no absolute relative reference; those references with the needed energy to be genuine SR effects. The alternative was include relativistic mass. This makes movement in the universe, ambiguous, since we cannot do proper energy balances, to know every object's absolute kinetic energy and relativistic mass; E=MC2. This knowledge might change the universal energy balance and energy density; find a center.

Getting back to zero

Say 1/0=infinity and 10/0=infinity. This means 1/0=10/0. If multiply both sides by 0, we get 1=10. This cannot happen in space-time, but it is possible if space and time were not tethered in the three legged race of space-time. I move in time=1 and space=10 as two steps since they do not have to race together but end together in a strange place in space and time where 10=1; intersect.

 

[Polymath257]

Above I was trying to do this from memory and forgot the extra square root.

In the twin paradox, one twin is stationary and the other twin leaves the earth, on a spaceship, that requires fuel conversion to propulsion, to gain the kinetic energy for the ship, so the ship can reach the needed relativistic velocity.

It is NOT the fuel usage that is the difference. it is the fact that one twin experiences an *acceleration* that the other does not: when the non-Earth twin turns around.

It is quite legitimate to have the 'moving twin' simply going past at a substantial fraction of the speed of light at the beginning of the experiment and simply moving past at the end. The ages will still differ because only one twin experiences that acceleration.

Although both references may appear to see each other the same way; relative reference, one reference is an illusion reference, since both references did not use energy to gain genuine relativistic changes. E=MC2 equates the relativistic mass change to the fuel energy conversion to kinetic energy. This is imaginary energy in the stationary relative earth reference. Only the moving twin ages since he had genuine energy needed for relativistic mass and time dilation; age slower. He may have expected to see his brother the same age, due to relative reference, but he saw an old man, since his brother did not have real energy based SR time dilation.

No, that is not how things work in special relativity.

First, there is no such thing as absolute motion in SR. The 'moving twin' can legitimately have *always* been moving at that speed relative to the Earth.

So it is NOT the 'energy need' that makes the relevant difference in aging. If the 'moving' twin never returned, both would see the other as aging slower than themselves.

When experiments were done, with radioactive decay in particle accelerators, the radioactive particles were supplied magnetic energy for conversion into kinetic energy, from an electric power source; got an electric bill. If we were sitting on these particles, we may appear to see the lab move, but that would be an illusion due to our own relativistic energy.

Not at all. Once again, there is no such thing as absolute motion in SR: there *is* such a thing as acceleration, though. In GR, even that gets replaced by 'gravity'.

This application of energy conservation to Special Relativity; I used to mention this years ago, caused some in physics to want to play down relativistic mass, so they can assume only relative references and no absolute relative reference; those references with the needed energy to be genuine SR effects. The alternative was include relativistic mass. This makes movement in the universe, ambiguous, since we cannot do proper energy balances, to know every object's absolute kinetic energy and relativistic mass; E=MC2. This knowledge might change the universal energy balance and energy density; find a center.

Again, not how SR deals with things. Uniform motion (no acceleration) is only defined *relative* to other things.

Relativistic mass is, agreed, a bit of an anachronism. But that factor on the mass does have real consequences, as in the case of proton collisions.

Also, there is no such thing as 'absolute energy': there is only energy as measured in some frame. THAT is always conserved in SR. But, if you change frames to something in motion relative to the first frame, the actually measured energies may be quite different. That said, the total energy (inclusing relativistic mass) will be conserved in the second frame as well.

Getting back to zero

Say 1/0=infinity and 10/0=infinity. This means 1/0=10/0. If multiply both sides by 0, we get 1=10. This cannot happen in space-time, but it is possible if space and time were not tethered in the three legged race of space-time. I move in time=1 and space=10 as two steps since they do not have to race together but end together in a strange place in space and time where 10=1; intersect.

No. 1/0 is undefined. If you are taking *limits* in calculus, it gives an infinite limit, but the ratio itself isn't defined.

 

[wellwisher]

It is NOT the fuel usage that is the difference. it is the fact that one twin experiences an *acceleration* that the other does not: when the non-Earth twin turns around.

It is quite legitimate to have the 'moving twin' simply going past at a substantial fraction of the speed of light at the beginning of the experiment and simply moving past at the end. The ages will still differ because only one twin experiences that acceleration.

No, that is not how things work in special relativity.

First, there is no such thing as absolute motion in SR. The 'moving twin' can legitimately have *always* been moving at that speed relative to the Earth.

So it is NOT the 'energy need' that makes the relevant difference in aging. If the 'moving' twin never returned, both would see the other as aging slower than themselves.

Not at all. Once again, there is no such thing as absolute motion in SR: there *is* such a thing as acceleration, though. In GR, even that gets replaced by 'gravity'.

Again, not how SR deals with things. Uniform motion (no acceleration) is only defined *relative* to other things.

Relativistic mass is, agreed, a bit of an anachronism. But that factor on the mass does have real consequences, as in the case of proton collisions.

Also, there is no such thing as 'absolute energy': there is only energy as measured in some frame. THAT is always conserved in SR. But, if you change frames to something in motion relative to the first frame, the actually measured energies may be quite different. That said, the total energy (inclusing relativistic mass) will be conserved in the second frame as well.


No. 1/0 is undefined. If you are taking *limits* in calculus, it gives an infinite limit, but the ratio itself isn't defined.

Your explanation is a common mistake due to one simple oversight. Let me give you an example. Say have two rocket ships in relative motion in space, so we cannot tell how is who; who has the energy. The twist is the first ship has mass =x and the second ship has mass=2x. The velocity may appear relative, but the momentum cannot be, due to the difference in masses. We can show, who has the energy but the differences in mass if we billiard ball collide them.

If the ship with mass=x thinks it is in motion and it collides with the ship with mass 2x, transfer of momentum (light hits heavy); billiard ball, the final relative motion will be different from the scenario where the 2x ship hits the 1x mass ship; heavy hitting the light. What you said does work, but only with twins; masses are the same. There are very few things in the universe with exactly the same mass, so the twin assumption of the universal energy balance of the universe is off. Variable masses allow a way to find the center.

If the above case, if we know who was stationary, and who used fuel to get the relative velocity for both, we can predict the recoil that has to result, since the energy balance and momentum, with difference masses, can only go one way.

In the twin paradox, the earth twin does not get any extra energy. Only the moving or rocket twin has its kinetic energy increase. He is the 8-ball. His relativity starts to created some real effects, and not just relative illusion effects. This is why only the moving twin ages slower.

Acceleration is not part of Special Relativity. SR is more designed for constant velocity. We are comparing d/t versus d/t/t. The first is one part distance and one part time like space-time. The second is one part distance and two parts time like space-time plus independent time. This adds something else at the quantum level; extra time potential. This is reflected in relativistic mass. If we had a lens that could see relativistic mass we could see a new universe POV.

I used to do a fun analogy, called the Relative Reference Work Out. This workout will appeal to couch potatoes. All you do is sit in a comfortable chair, near a running track. You watch the runners, we will provide, and you pretend you are the moving frame and the runners on the track, are the stationary frame Using existing relative reference you can burn calories while daydreaming.


Back to zero

I think I figured out one key example where division, by a fraction, actually works in reality. This came to me last night. Say we start with 1 divided by 1/2 = 2.

If you look at a mother cell, ready to divide, with her extra bulk and her doubled DNA, we start with one cell, in an advanced state of labor. Next we will divide her by a half, to make two daughter cells. One cell can divide into two cells, and not just two halves like an apple, but into two living cells, since the two halves are full cells, all on their own.

Maybe life and consciousness, is where division by fractions starts to make sense in reality; overlap of separated space and time. Virus can replicate hundreds of exact copies, by division by a fraction. This only needs a healthy working cell's and its DNA to act as the operator for the fractional divider (and assembler); 1 virus divided by 1/10 = 100 virus; exact duplicates.

Memes are types of word virus that ca divide ands make new copies through neural division processes; thousands of the same meme using will and the dividers of social media. An example of division by zero is still on the back burner. The closest is the primordial atom and the relativity of space-time, as more and more frames appear with less and less GR; reference division by expansion.

 

[Polymath257]

Your explanation is a common mistake due to one simple oversight. Let me give you an example. Say have two rocket ships in relative motion in space, so we cannot tell how is who; who has the energy. The twist is the first ship has mass =x and the second ship has mass=2x. The velocity may appear relative, but the momentum cannot be, due to the difference in masses. We can show, who has the energy but the differences in mass if we billiard ball collide them.

Huh? The momentum is determined in whatever frame you choose. It is also relative to motion in that frame.

When you say one ship has mass x and the other has mass 2x, do you mean rest mass or relativistic mass? The results will differ, but the method of calculation is much the same.

If the ship with mass=x thinks it is in motion and it collides with the ship with mass 2x, transfer of momentum (light hits heavy); billiard ball, the final relative motion will be different from the scenario where the 2x ship hits the 1x mass ship; heavy hitting the light.

In both cases, there will be a transfer of momentum. In the frame where the x mass is at rest initially, it will begin to move after the collision. The 2x mass will decrease in velocity. The end result is that *total* momentum (using the relativistic formula for momentum) will be conserved.

In the case where the 2x mass is at rest initially, the 2x mass will start to move and the x mass will be moving slower, again in such a way that the total momentum is conserved.

In the center of momentum frame, the x mass comes in, reverses direction and keeps the same velocity. So does the 2x mass.

What you said does work, but only with twins; masses are the same. There are very few things in the universe with exactly the same mass, so the twin assumption of the universal energy balance of the universe is off. Variable masses allow a way to find the center.

The appropriate frame to do the calculations for collisions is the center of momentum frame, whether the two particles have equal and opposite momentum. In that frame, the collision looks identical for the two situations (as it should).

If the above case, if we know who was stationary, and who used fuel to get the relative velocity for both, we can predict the recoil that has to result, since the energy balance and momentum, with difference masses, can only go one way.

Um, no. There is no such thing as 'stationary'. ALL motion (or lack of motion) is relative: you get to choose the frame you want to do calculations in and ALL frames give consistent results using Lorentz transformations to shift between frames.

So, in the case where a rest mass of 2x hits a rest mass of x, neither rest frame is the center of momentum frame. You *can* do the calculation in any frame, but it is considerably easier in the center of momentum frame. And in *that* frame, the two collisions are identical.

In the twin paradox, the earth twin does not get any extra energy. Only the moving or rocket twin has its kinetic energy increase. He is the 8-ball. His relativity starts to created some real effects, and not just relative illusion effects. This is why only the moving twin ages slower.

Acceleration is not part of Special Relativity. SR is more designed for constant velocity. We are comparing d/t versus d/t/t. The first is one part distance and one part time like space-time. The second is one part distance and two parts time like space-time plus independent time. This adds something else at the quantum level; extra time potential. This is reflected in relativistic mass. If we had a lens that could see relativistic mass we could see a new universe POV.

Actually, SR *can* deal with accelerations, although it is usually not taught at the elementary level. The acceleration is always done using the proper time of the particle.

I used to do a fun analogy, called the Relative Reference Work Out. This workout will appeal to couch potatoes. All you do is sit in a comfortable chair, near a running track. You watch the runners, we will provide, and you pretend you are the moving frame and the runners on the track, are the stationary frame Using existing relative reference you can burn calories while daydreaming.

Well, if those runners didn't have to deal with friction, they would need to expend no energy to stay in motion at a uniform speed.

 

[Balthazzar]

Question: Mathematics have an infinite ability both ways for calculations. My question is why is a negative zero not useful in equations? I'm asking based on the nature of opposites, which zero does not appear to have, due to it being neutral and not a true number, yet it's also most powerful. Is this due to simplicity of calculations or because utilizing a negative counterpart is irrelevant?

 

[Heyo]

Question: Mathematics have an infinite ability both ways for calculations. My question is why is a negative zero not useful in equations? I'm asking based on the nature of opposites, which zero does not appear to have, due to it being neutral and not a true number, yet it's also most powerful. Is this due to simplicity of calculations or because utilizing a negative counterpart is irrelevant?

I have a digital thermometer that displays "0" and "-0", the latter for temperatures between -0.5 and 0 (rounding up).

 

[Polymath257]

Question: Mathematics have an infinite ability both ways for calculations. My question is why is a negative zero not useful in equations? I'm asking based on the nature of opposites, which zero does not appear to have, due to it being neutral and not a true number, yet it's also most powerful. Is this due to simplicity of calculations or because utilizing a negative counterpart is irrelevant?

The negative of x, -x, is defined to be the number y such that x+y=0. In other words, -x is the additive inverse of x. Here, 0 is defined to be the number where x+0=x for all numbers x.

For x=0, we see that 0+0=0, so -0=0. It really is that simple: the negative of 0 is 0.

We can do a similar thing with multiplication. The multiplicative inverse of x is the number y with x*y=1, if such exists. Here, 1 is the number with x*1=x for all x. So, 1*1=1 and we see that the multiplicative inverse of 1 is 1.

Note: we also find that 0 has no multiplicative inverse since 0*y=0 for all numbers y. This is why division by 0 is undefined.

 

[Twilight Hue]

Nothing by any other name is something.

 

[Balthazzar]

The negative of x, -x, is defined to be the number y such that x+y=0. In other words, -x is the additive inverse of x. Here, 0 is defined to be the number where x+0=x for all numbers x.

For x=0, we see that 0+0=0, so -0=0. It really is that simple: the negative of 0 is 0.

We can do a similar thing with multiplication. The multiplicative inverse of x is the number y with x*y=1, if such exists. Here, 1 is the number with x*1=x for all x. So, 1*1=1 and we see that the multiplicative inverse of 1 is 1.

Note: we also find that 0 has no multiplicative inverse since 0*y=0 for all numbers y. This is why division by 0 is undefined.

So why not a double negative? The 0 still multiplies by 10 negatives on the whole number. I don't get it.

 

[Polymath257]

So why not a double negative? The 0 still multiplies by 10 negatives on the whole number. I don't get it.

For any x, -(-x)=x.

Again, the defining property of, say, -3 is that 3+(-3)=0. Since (-3)+3=0, we see that -(-3)=3.

I have no idea what you mean by "The 0 still multiplies by 10 negatives on the whole number".

 

[Balthazzar]

For any x, -(-x)=x.

Again, the defining property of, say, -3 is that 3+(-3)=0. Since (-3)+3=0, we see that -(-3)=3.

I have no idea what you mean by "The 0 still multiplies by 10 negatives on the whole number".

- 3 + 0 = -30 which is a power of 10 times that of - 3.
-3 + - 0 would still be - 3? Is this correct? Why doesn't mathematics work in opposites with the zero?

It's a philosophical question dealing with hard mathematics. I'm looking for the equilibrium for the 0, specifically. In-between heat and cold is a balance, between pleasure and pain is another balance, so why is 0 alone and reliant on the others to add value to it and its usage?

At this point I'm looking at zero as if it were playing the role of the universe and all other numbers exist inside the zero infinitely.

 

[Polymath257]

- 3 + 0 = -30 which is a power of 10 times that of - 3.

I’m, no. -3+0=-3. Why would you think it is -30?

-3 + - 0 would still be - 3? Is this correct? Why doesn't mathematics work in opposites with the zero?

It does. (-3)+(-0)=-(3+0)=-3. Also, -3+0=-3, since-0=0.

It's a philosophical question dealing with hard mathematics. I'm looking for the equilibrium for the 0, specifically. In-between heat and cold is a balance, between pleasure and pain is another balance, so why is 0 alone and reliant on the others to add value to it and its usage?

Because it is that balance.

At this point I'm looking at zero as if it were playing the role of the universe and all other numbers exist inside the zero infinitely.

Huh?

 

[Balthazzar]

I’m, no. -3+0=-3. Why would you think it is -30?

It does. (-3)+(-0)=-(3+0)=-3. Also, -3+0=-3, since-0=0.

Because it is that balance.

Huh?

Negative 3 plus 0 after, equates to negative 30. If a negative zero were applied, would it still equate to a negative 30 or something else, understanding that there is no negative for the zero? Anti matter vs matter is where the inquiry came concerning the 0. I never knew it existed until it did. I don't think a negative zero has an existence in mathematics, so I was questioning why?

 

[Balthazzar]

Infinity is self-contained, so a zero + and a Zero - applied inside the zero itself both ways would appropriately define infinity as a self-contained reality, particularly utilizing mathematics to illustrate the concept. If zero represents the universe then it makes sense using this paradigm.