If 0+0=0 and 0-0=0, 0x0=0, Why is 0/0 indeterminate?

[anotherlife]

Try not to get too technical, but can anyone explain this in common English?
I went home and thought about it last night, but for the life of me, I can't understand why if it applies to division, it doesn't apply to the rest. What is different about division that doesn't allow that?

We can do it by example, how about this, cut up a bread to infinitely thin slices. Then you will need to take away infinitely many slices to consume your original loaf of bread so the result of your division is negative infinity.

Now take many infinitely thin slices to make up your original loaf of bread. You wil need all the infinitely many slices to reconstruct your loaf of bread so your result is positive infinity.

But what if your slices are not infinitely thin but zero thin. Since 0+0=0, not even infinitely many slices will give you back your bread. This is why the division by zero is a special case, breaks every number even infinity itself.

So it is axiomatically defined as error. It's effect is to cause a discontinuity in everything it touches, a singularity if you like. The division by zero is frequently used in mathematics in many calculations for example the estimation of system stability in the general sense, where the locations of such divisions are called the poles of the system.

Dividing by zero? It's common to multiply two sides of an equation by zero, but divide? Can't think of when that would be legitimate.

You can think of it as two polynomials, one dividing the other. The ratio of the two polynomials is the system output. The numerator polynomial is the forward behavior of the system, and the denomerator polynomial is the feedback behavior of the system, a memory, if you like. Each of the polynomials are linear combinations of the system input raised to various powers. This model describes every system in the universe generally. To calculate the physical poles of the system, you equate the enumerated result of the denominator polynomial to zero, i.e. you assume that you are inside a singularity of the system. You work backwards from this zero equation to find out what sort of system inputs could be capable to produce the singularity. So to answer your question in short, you don't do the division by zero but assume it then work backwards from that assumption to find the input values that can cause it.

 

[anotherlife]

In the OP Old Lady posted a logical question concerning our mathematical constructs. It was answered by several people with pretty good analytical posts. Yours, PC, was not among them.

There are many questions in our understanding of mathematics that seem to have no answers, like why some fundamental values, such as Pi, have no repeating patterns in their value, and go one forever. There may be a mathematician out there that can answer that, and it may be that the majority of us will never understand his answer. But these are good questions to consider, in their scientific context. Inserting religion of politics into the discussion is just a diversion and adds nothing.

Let me add, that there are altogether 3 mystery constants in mathematics. The popular pi, the self driving natural log base "e", and the differential matrix algebra "c". We know what the approximate value of pi and e is, but nobody knows the c. (In fact, I don't even understand the c and I am a math student, is there someone here who knows a reference paper of the c? Thanks.).

 

[Vikrant]

Try not to get too technical, but can anyone explain this in common English?
I went home and thought about it last night, but for the life of me, I can't understand why if it applies to division, it doesn't apply to the rest. What is different about division that doesn't allow that?

This is an excellent thread. I am not sure why someone was hurling abuses at you. Anyway, coming back to the topic, your question can be explained using elementary school arithmetic aka plain English. To understand, why you cannot divide a number with 0, you have to understand the relation between multiplication and division.

Let us take an example:
10 / 5 = 2

This means:
5 x 2 = 10

Now, let us see what happens when we attempt to divide 10 by 0:
10 / 0 = U
(Since we do not know the actual value of quotient, let us give it a value of U.)

This would mean:
0 x U = 10

This is not possible because you already know that 0 multiplied by any number is 0.

 

[BULLDOG]

Try not to get too technical, but can anyone explain this in common English?
I went home and thought about it last night, but for the life of me, I can't understand why if it applies to division, it doesn't apply to the rest. What is different about division that doesn't allow that?

It helps to think of the actual language and what you are doing: e.g., 6 / 3 = 2 means you have six apples and divide them into three groups, you have two apples in each group. But if you have six apples and divide them up into no groups ... and it becomes irrational because you can't divide something into nothingness.

Thanks!

If nothing else, just put it in the category of "that's just the way it is". Accept it and move on.

Not into solving that mystery today, are you? Fine. I'm curious; that okay with you?

Fine with me. Curiosity is a good thing.

 

[Vikrant]

Try not to get too technical, but can anyone explain this in common English?
I went home and thought about it last night, but for the life of me, I can't understand why if it applies to division, it doesn't apply to the rest. What is different about division that doesn't allow that?

We can do it by example, how about this, cut up a bread to infinitely thin slices. Then you will need to take away infinitely many slices to consume your original loaf of bread so the result of your division is negative infinity.

Now take many infinitely thin slices to make up your original loaf of bread. You wil need all the infinitely many slices to reconstruct your loaf of bread so your result is positive infinity.

But what if your slices are not infinitely thin but zero thin. Since 0+0=0, not even infinitely many slices will give you back your bread. This is why the division by zero is a special case, breaks every number even infinity itself.

So it is axiomatically defined as error. It's effect is to cause a discontinuity in everything it touches, a singularity if you like. The division by zero is frequently used in mathematics in many calculations for example the estimation of system stability in the general sense, where the locations of such divisions are called the poles of the system.

Dividing by zero? It's common to multiply two sides of an equation by zero, but divide? Can't think of when that would be legitimate.

It is not quite as simple. This is why I was confounded that someone was making fun of OP.

You can divide a number with 0. There is nothing invalid about it. It is the result which cannot be defined. So to manage this situation, you assign a value called limit. The higher the value of the limit is, closer you are approaching to the infinity (defined to undefined). This concept gave birth to the idea of limit in calculus. However, this is just the beginning of our attempt at managing infinity.

It gets quite complicated if you dive deeper into it. If you do not mind getting headache, read some papers on Ramanujan's Infinite Series Identities.

 

[Vikrant]

In the OP Old Lady posted a logical question concerning our mathematical constructs. It was answered by several people with pretty good analytical posts. Yours, PC, was not among them.

There are many questions in our understanding of mathematics that seem to have no answers, like why some fundamental values, such as Pi, have no repeating patterns in their value, and go one forever. There may be a mathematician out there that can answer that, and it may be that the majority of us will never understand his answer. But these are good questions to consider, in their scientific context. Inserting religion of politics into the discussion is just a diversion and adds nothing.

... but nobody knows the c. (In fact, I don't even understand the c and I am a math student, is there someone here who knows a reference paper of the c? Thanks.).

I went for a job/contract interview/screening at the beginning of this year in Palo Alto, CA. The company is a well known manufacturer of medical devices. They wanted to talk to me about matrix. I was not very pleased as I had to drive for over 2 hours in the infamous Bay Area traffic to get there.

I think the reason you cannot calculate the value of C is following:
d/dt(CA) = (C)dA/dt

I have been out of school for decades now so go easy on me But I have a feeling you already knew the answer.

 

[cnelsen]

Try not to get too technical, but can anyone explain this in common English?
I went home and thought about it last night, but for the life of me, I can't understand why if it applies to division, it doesn't apply to the rest. What is different about division that doesn't allow that?

We can do it by example, how about this, cut up a bread to infinitely thin slices. Then you will need to take away infinitely many slices to consume your original loaf of bread so the result of your division is negative infinity.

Now take many infinitely thin slices to make up your original loaf of bread. You wil need all the infinitely many slices to reconstruct your loaf of bread so your result is positive infinity.

But what if your slices are not infinitely thin but zero thin. Since 0+0=0, not even infinitely many slices will give you back your bread. This is why the division by zero is a special case, breaks every number even infinity itself.

So it is axiomatically defined as error. It's effect is to cause a discontinuity in everything it touches, a singularity if you like. The division by zero is frequently used in mathematics in many calculations for example the estimation of system stability in the general sense, where the locations of such divisions are called the poles of the system.

Dividing by zero? It's common to multiply two sides of an equation by zero, but divide? Can't think of when that would be legitimate.

You can think of it as two polynomials, one dividing the other. The ratio of the two polynomials is the system output. The numerator polynomial is the forward behavior of the system, and the denomerator polynomial is the feedback behavior of the system, a memory, if you like. Each of the polynomials are linear combinations of the system input raised to various powers. This model describes every system in the universe generally. To calculate the physical poles of the system, you equate the enumerated result of the denominator polynomial to zero, i.e. you assume that you are inside a singularity of the system. You work backwards from this zero equation to find out what sort of system inputs could be capable to produce the singularity. So to answer your question in short, you don't do the division by zero but assume it then work backwards from that assumption to find the input values that can cause it.

Got it. Very cool.

 

[cnelsen]

Try not to get too technical, but can anyone explain this in common English?
I went home and thought about it last night, but for the life of me, I can't understand why if it applies to division, it doesn't apply to the rest. What is different about division that doesn't allow that?

We can do it by example, how about this, cut up a bread to infinitely thin slices. Then you will need to take away infinitely many slices to consume your original loaf of bread so the result of your division is negative infinity.

Now take many infinitely thin slices to make up your original loaf of bread. You wil need all the infinitely many slices to reconstruct your loaf of bread so your result is positive infinity.

But what if your slices are not infinitely thin but zero thin. Since 0+0=0, not even infinitely many slices will give you back your bread. This is why the division by zero is a special case, breaks every number even infinity itself.

So it is axiomatically defined as error. It's effect is to cause a discontinuity in everything it touches, a singularity if you like. The division by zero is frequently used in mathematics in many calculations for example the estimation of system stability in the general sense, where the locations of such divisions are called the poles of the system.

Dividing by zero? It's common to multiply two sides of an equation by zero, but divide? Can't think of when that would be legitimate.

It is not quite as simple. This is why I was confounded that someone was making fun of OP.

You can divide a number with 0. There is nothing invalid about it. It is the result which cannot be defined. So to manage this situation, you assign a value called limit. The higher the value of the limit is, closer you are approaching to the infinity (defined to undefined). This concept gave birth to the idea of limit in calculus. However, this is just the beginning of our attempt at managing infinity.

It gets quite complicated if you dive deeper into it. If you do not mind getting headache, read some papers on Ramanujan's Infinite Series Identities.

But wouldn't dividing by 0 be the same thing as, say, multiplying by infinity--i.e., something we can't do?

1 / 1 = 1
1 / .1 = 10
1 / .01 = 100
1 / .001 = 1000
...
[approaching zero]
1 / .0000000000001 = 1,000,000,000,000

Just like the asymptote never actually touches the axis, we can't actually divide by zero, only, by taking the differential, see where we are going?

 

[Iceweasel]

The universe coming into existence from nothing is actually supported by the math.

No it isn't. You bought snake oil.

To learn these things requires reading, or even these days at least watching an hour long video online of which Lawrence Krauss and others like Michio Kaku have many, but reading and learning are kryptonite to conservatives.

Ignorance is the savior in conservative thought. Talking snakes are science.

You have no evidence to support your claim or you would have posted it. Smug arrogant bullshit is the life's blood of the libteral. You think you can bully people into agreeing with your dumb ass assertions?

 

[Vikrant]

Try not to get too technical, but can anyone explain this in common English?
I went home and thought about it last night, but for the life of me, I can't understand why if it applies to division, it doesn't apply to the rest. What is different about division that doesn't allow that?

We can do it by example, how about this, cut up a bread to infinitely thin slices. Then you will need to take away infinitely many slices to consume your original loaf of bread so the result of your division is negative infinity.

Now take many infinitely thin slices to make up your original loaf of bread. You wil need all the infinitely many slices to reconstruct your loaf of bread so your result is positive infinity.

But what if your slices are not infinitely thin but zero thin. Since 0+0=0, not even infinitely many slices will give you back your bread. This is why the division by zero is a special case, breaks every number even infinity itself.

So it is axiomatically defined as error. It's effect is to cause a discontinuity in everything it touches, a singularity if you like. The division by zero is frequently used in mathematics in many calculations for example the estimation of system stability in the general sense, where the locations of such divisions are called the poles of the system.

Dividing by zero? It's common to multiply two sides of an equation by zero, but divide? Can't think of when that would be legitimate.

It is not quite as simple. This is why I was confounded that someone was making fun of OP.

You can divide a number with 0. There is nothing invalid about it. It is the result which cannot be defined. So to manage this situation, you assign a value called limit. The higher the value of the limit is, closer you are approaching to the infinity (defined to undefined). This concept gave birth to the idea of limit in calculus. However, this is just the beginning of our attempt at managing infinity.

It gets quite complicated if you dive deeper into it. If you do not mind getting headache, read some papers on Ramanujan's Infinite Series Identities.

But wouldn't dividing by 0 be the same thing as, say, multiplying by infinity--i.e., something we can't do?

1 / 1 = 1
1 / .1 = 10
1 / .01 = 100
1 / .001 = 1000
...
[approaching zero]
1 / .0000000000001 = 1,000,000,000,000

Just like the asymptote never actually touches the axis, we can't actually divide by zero, only, by taking the differential, see where we are going?

You are correct.

I was speaking from the perspective of ALU (Arithmetic Logic Unit) algorithm. In ALU, you only have two logic to carry out arithmetic calculations; they are Boolean Addition and Boolean Subtraction. Boolean Addition is used to perform multiplications and additions. Boolean Subtraction is used to perform divisions and subtractions.

So when you are dividing a dividend by a divisor, Boolean Subtraction simply keeps subtracting divisor from dividend till it can no longer subtract from the dividend. The count of subtraction performed is your quotient.

As you can see, when you divide a number with 0, the logic will go in an infinite loop till the overflow throws an exception.

 

[OldLady]

This is in response to the deeply indoctrinated disciples that believe matter can come from nothing? Good luck with that, you're better off with a Moonie.

I really liked that not-so-subtle dig.

So where did the Universe come from when there was nothing in the beginning? Not a sermon, just a question?

What is truly astounding is how closely the biblical version of events parallels what modern science believes.

Now...about the origin of the universe.....and the fact that modern science now accepts the very same order of events as Genesis.....

1. God’s first command in Genesis is “Let there be light.” Nor is this the only introduction of light in the Genesis creation account, but it is the first, it represents the beginning of the formation of our solar system. And that was ‘The Big Bang’…some 13,700 million years ago. Quite an event…it lasted just 10 to the minus 35th seconds, beginning the universe, generating time and space, as well as all the matter and energy that the universe would ever, ever, contain! Big Bang…explosion….energy….light. But no atoms to form the sun for some time. Light…but no sun? So says science. And so says Genesis. Parker, “The Genesis Enigma,” chapter two.

a. For reference, Genesis 1, verses 1-4: In the beginning God created the heaven and the earth. And the earth was without form, and void; and darkness was upon the face of the deep. And the Spirit of God moved upon the face of the waters. And God said, Let there be light: and there was light. And God saw the light, that it was good: and God divided the light from the darkness.



2. Modern science has largely revealed the earth’s history with respect to the land and the seas. Coincidently, the first chapter of the Bible relates a formation, a creation narrative, strangely similar to scientific understanding.


a. Genesis 1: 6-10…”And God said, Let there be a firmament in the midst of the waters, and let it divide the waters from the waters. And God made the firmament, and divided the waters which were under the firmament from the waters which were above the firmament: and it was so. And God called the firmament Heaven. And the evening and the morning were the second day. And God said, Let the waters under the heaven be gathered together unto one place, and let the dryland appear: and it was so. And God called the dry landEarth; and the gathering together of the waters called he Seas: and God saw that it wasgood.


b. “The formation of the sea as well as the land is chosen as the second stage in the creation on the Bible’s first page. Modern science reveals that land and sea certainly were in place before the next stage in the scientific account of the history of the universe.” Parker, “The Genesis Enigma,” p.54. What a coincidence….or confluence.


Curious, the author of Genesis lived in a landlocked region; and Moses wandered in the desert, not along the coast. Yet…sea and land appear in this prominent position in Genesis. Must be a coincidence….



3. The opening page of Genesis asserts that plant life appeared after the seas were formed, and names specifically, grass, herbs and fruit trees. According to the author of Genesis, this is the stage where life actually begins: this is the first mention life of any kind. Plant life. Yet, the simple forms of life that are considered plant life were not discovered until a couple of millennia after Genesis was completed. So…how come Genesis mentions grass, herbs, and fruit trees at precisely this moment on the creation narrative? Parker, “The Genesis Enigma,” chapter four.


a. Genesis 1: 11-12 And God said, Let the earth bring forth grass, the herb yielding seed,and the fruit tree yielding fruit after his kind, whose seed is in itself, upon the earth: and it was so. And the earth brought forth grass, and herb yielding seed after his kind, and the tree yielding fruit, whose seed was in itself, after his kind: and God saw that it was good.


b. “ From about 400 million years back to 600 million years, all kinds of complex multicellular life would have been confined to the waters of the earth….Our world's ecosystems depend upon photosynthesis to construct the fuel that all life runs on; in an ancient world with conditions similar to today's, you would need plants (as organisms that can make complex "fuel" molecules using simple building blocks and energy available from the environment, plants are known as one type of autotrophs, or "self-feeders") to evolve first, or there would be no bottom link to the food chain.” Biology of Animals & Plants - Origins & History of Life on Earth



4. Track the events in the creation account of Genesis and it’s amazing how closely the events conform to the current view of modern science. An explosion- the universe – oceans/land - plants- …And next, in verse 20, we find: And God said, Let the waters bring forth abundantly the moving creature that hath life, and fowl that may fly above the earth in the open firmament of heaven.


Kind of unusual…since the author of Genesis, and, if we are to believe that the first one to speak those words, Moses, didn’t really live in a habitat that one might call ‘sea side.’


Would have been understandable if this space in the Bible had, instead, have focused on the numbers of land mammals, birds, or insects found in ancient Israel, wouldn’t it? But, instead, marine organisms are specifically named: ‘Let the waters bring forth abundantly the moving creature that hath life,…’


Wouldn’t it be interesting if science find lots and lots of marine organisms extant at this point? Imagine if Genesis actually parallels the history of life on earth as expounded by science. Be a heck of a coincidence.

a. A truly important development took place some 521 million years ago, in the geological period known as the Cambrian. “The most abundant and diverse animals of Cambrian time were the trilobites. Trilobites had long antennae, compound eyes, many jointed legs, and a hard exoskeleton like many of their modern arthropod relatives, such as lobsters, crabs, and insects. The Cambrian is sometimes called the "Age of Trilobites"…” Redirect


b. No earlier fossils were found during Darwin’s lifetime: “If the theory [evolution] be true it is indisputable that before the lowest Cambrian stratum was deposited ... the world swarmed with living creatures. [Yet] to the question why we do not find rich fossiliferous deposits belonging to these earliest periods. . . I can give no satisfactory answer. The case at present must remain inexplicable.” http://www.paleosoc.org/Oldest_Fossil.pdf

....life at this stage, about 500 million years ago, was entirely marine.

How could the Genesis writer have gotten this right?

That writer…he’s landlocked, knows little of diversity….what are the odds that ‘chance’ is the answer?


What are the odds?



5. The sequence of events from the creation of the universe, to the present, begin with great explosion that produces the universe, including the earth. The earth cools enough for oceans to form. The first life is plant life, able to photosynthesize, and add oxygen to the atmosphere. All sorts of simple non-plants fill the seas, most wormlike, with soft bodies. Along come the trilobites, hugely advanced, with hard bodies…and most amazingly, with true eyes! This makes them the primary predators….but, imposes enormous evolutionary pressure on the other organisms. The result is the Cambrian explosion, lots of small organisms with defensive armor and hard exoskeletons, some 521 million years ago. So says modern science.


a. “…Genesis shows remarkable accuracy when compared to the scientific story of life’s evolutionary journey. Here, the Genesis writer envisioned great creatures evolving from those tiny Cambrian forms, eventually making their way out of the sea….Genesis seems to have picked out all the events of the highest order of importance, and put them in the right order….I don’t know the odds against such a parallel- against making a successful guess at the scientific orthodoxy of three thousand year into the future from a knowledge base of nothing- but they must be extraordinarily long.” Parker, Op. Cit., p.163-164.


b. An interesting sidelight is the ‘evolution of the Bible’ itself. Christians have incorporated a great deal of science’s process. Early in the 20th century, the Scofield Reference Bible was published. This was a new version of the King James Bible with which added a note to Genesis, suggesting what is called the “gap theory.’ It allows that millions of years could have passed between God’s creation of the heavens and the earth, thereby freeing Genesis from the literal six-day process. “What it left was a series- the same series- of timeless events; and it is these that match the scientific account of life’s history.” Parker, “The Genesis Enigma,” p. 160.


6. Unavoidable is the recognition that, once the restrictions due to the ‘six-day’ view are removed, the order of events established by modern science conform to the sequence in the first chapter of Genesis, written millennia earlier: light from an explosion (the Big Bang), universe/earth formed, the seas from the cooling earth, plants as the first life forms; abundant sea life (the Cambrian explosion), the (evolution) of the flora and fauna we see today. Neat, eh?

Lucky guess by the author of the creation account of Genesis?


7. If it is not evidence for the God, then the author of Genesis 1, or Moses, perhaps, must have understood that the universe formed first, then the seas appeared on earth, and that life forms were photosynthetic. Following that, he had to have realized that an eye evolved in an early animal in the geological past, which triggered the evolution of all the major groups of animals that exist today. Still further, he must have felt that all of this occurred in the seas, before animals moved onto land, and only when they did move out of the water did mammals and birds evolve.
See Parker's "The Genesis Enigma"



The Old Testament was written, although not compiled, almost three millennia ago. It is extraordinary that the writer of the creation account in Genesis, chapter one, got it right in his exposition of the series of events: his sequence turns out to be scientifically accurate in terms of contemporary knowledge.


Wow! What an incredibly lucky guess! What a considerable stroke of good fortune!


The alternative explanation is divine intervention.

That IS fascinating. Eastern spiritual thought also seems to intuitively understand particle physics, the cosmic dance of the universe. This is my (probably cracked) theory: Humankind has been on this Earth for a couple hundred thousand years and we are finding evidence of older and older civilizations every year. I believe that at one time there were civilizations as advanced as ours in their understanding of science and they were so far back in time that evidence of their existence has vanished from the record. It lives on, though, in the oldest of the stories.

Hmmmmmm.................. We would have found the equivalent of their Coke bottles. But most of our ancestors were just as smart as us, just had not yet developed writing to communicate from generation to generation.

You think we would have found their Coke bottles? I'm not so sure. But the Old People knew stuff, that's for sure.

 

[OldLady]

Try not to get too technical, but can anyone explain this in common English?
I went home and thought about it last night, but for the life of me, I can't understand why if it applies to division, it doesn't apply to the rest. What is different about division that doesn't allow that?

We can do it by example, how about this, cut up a bread to infinitely thin slices. Then you will need to take away infinitely many slices to consume your original loaf of bread so the result of your division is negative infinity.

Now take many infinitely thin slices to make up your original loaf of bread. You wil need all the infinitely many slices to reconstruct your loaf of bread so your result is positive infinity.

But what if your slices are not infinitely thin but zero thin. Since 0+0=0, not even infinitely many slices will give you back your bread. This is why the division by zero is a special case, breaks every number even infinity itself.

So it is axiomatically defined as error. It's effect is to cause a discontinuity in everything it touches, a singularity if you like. The division by zero is frequently used in mathematics in many calculations for example the estimation of system stability in the general sense, where the locations of such divisions are called the poles of the system.

Dividing by zero? It's common to multiply two sides of an equation by zero, but divide? Can't think of when that would be legitimate.

You can think of it as two polynomials, one dividing the other. The ratio of the two polynomials is the system output. The numerator polynomial is the forward behavior of the system, and the denomerator polynomial is the feedback behavior of the system, a memory, if you like. Each of the polynomials are linear combinations of the system input raised to various powers. This model describes every system in the universe generally. To calculate the physical poles of the system, you equate the enumerated result of the denominator polynomial to zero, i.e. you assume that you are inside a singularity of the system. You work backwards from this zero equation to find out what sort of system inputs could be capable to produce the singularity. So to answer your question in short, you don't do the division by zero but assume it then work backwards from that assumption to find the input values that can cause it.

Are you an engineer? Quite awesome how the rules of math get more involved than James Joyce.

 

[OldLady]

Anybody being an asshole to OldLady can suck a fuckin cock through a straw made of pvc

It's okay now, G.T. Just a couple grumpies yesterday morning before I was properly mentally prepared. People here are so smart, it's amazing. Loving it.

 

[PK1]

Try not to get too technical, but can anyone explain this in common English?
I went home and thought about it last night, but for the life of me, I can't understand why if it applies to division, it doesn't apply to the rest. What is different about division that doesn't allow that?

Why is 0/0 indeterminate?

That's actually a very interesting Q.
First of all, it's only mathematics and may not explain some conceptual philosophical ideas, esp those that cannot be measured, such as "infinity" or "nothing".

If you can think of a "nothing", then it's no longer nothing. And "infinity" is impossible to comprehend. Therefore, both concepts are in the same meaningless boat (i.e., undefined, indeterminate, or error), when it comes to explaining.
Such as 0/0 = ??

Math is a measurement tool in science, which is about explaining patterns.
Using math patterns, 0/0 = 1 or 0.
Which? In either case or "mathematical explanation", you're dealing with meaningless nothingness or infinity.

"Something from nothing" is irrational in both science & religion; both stem from philosophy, albeit one is more logical than the other.

 

[OldLady]

Try not to get too technical, but can anyone explain this in common English?
I went home and thought about it last night, but for the life of me, I can't understand why if it applies to division, it doesn't apply to the rest. What is different about division that doesn't allow that?

Why is 0/0 indeterminate?

That's actually a very interesting Q.
First of all, it's only mathematics and may not explain some conceptual philosophical ideas, esp those that cannot be measured, such as "infinity" or "nothing".

If you can think of a "nothing", then it's no longer nothing. And "infinity" is impossible to comprehend. Therefore, both concepts are in the same meaningless boat (i.e., undefined, indeterminate, or error), when it comes to explaining.
Such as 0/0 = ??

Math is a measurement tool in science, which is about explaining patterns.
Using math patterns, 0/0 = 1 or 0.
Which? In either case or "mathematical explanation", you're dealing with meaningless nothingness or infinity.

"Something from nothing" is irrational in both science & religion; both stem from philosophy, albeit one is more logical than the other.

Thanks to the marvelous brains on this board, I grasp the "can't reverse it" explanation and the "what are you dividing by--you don't know so you can't" explanation. That second one makes the most sense to me, although I'm sure they're both practical rules. THANK YOU ALL!
I think like me, PK1, you might be in for some surprises if you look at quantum physics these days; they're saying quantum particles do randomly spring from nothing and then disappear again. That's pretty counterintuitive to me, but I'm trying to catch up.

 

[PK1]

PK1, you might be in for some surprises if you look at quantum physics these days; they're saying quantum particles do randomly spring from nothing and then disappear again. That's pretty counterintuitive to me, but I'm trying to catch up.

Science measures what it can perceive, and beyond that, some scientists theorize entities of matter & how they behave (or how patterns developed over spacetime). The better scientists are agnostic & have a background in philosophy, or specifically for quantum mechanics research, in philosophy of physics.

Spring from "nothing"?
Just because you can't perceive it does not mean there's nothing there! Many theoretical physicists believe in "dark matter/energy" that supposedly comprises 96% of all matter. Then there's anti-matter, etc.

 

[OldLady]

PK1, you might be in for some surprises if you look at quantum physics these days; they're saying quantum particles do randomly spring from nothing and then disappear again. That's pretty counterintuitive to me, but I'm trying to catch up.

Science measures what it can perceive, and beyond that, some scientists theorize entities of matter & how they behave (or how patterns developed over spacetime). The better scientists are agnostic & have a background in philosophy, or specifically for quantum mechanics research, in philosophy of physics.

Spring from "nothing"?
Just because you can't perceive it does not mean there's nothing there! Many theoretical physicists believe in "dark matter/energy" that supposedly comprises 90% of all matter. Then there's anti-matter, etc.

I tend to agree with that, generally. In order to be cautious, they only admit to what they can observe or prove in some way. (Same with archeology, where they keep moving back the "first" civilization and "first" man, with each discovery.) They keep finding more and more. Krauss said they don't know why a "vacuum" in space still has weight. I guess it would be too simple and obvious to just guess that's because it's not empty, that there is indeed "something" there we haven't figured out yet. That "something" perhaps is where quantum particles spring from in their random dance.
I know nothing about dark or anti-matter, black holes, even apparently about energy. This thread makes me aware that I'm pretty damned dumb, actually, but it's fascinating and gives me quite the reading list for rainy days.

 

[anotherlife]

Try not to get too technical, but can anyone explain this in common English?
I went home and thought about it last night, but for the life of me, I can't understand why if it applies to division, it doesn't apply to the rest. What is different about division that doesn't allow that?

We can do it by example, how about this, cut up a bread to infinitely thin slices. Then you will need to take away infinitely many slices to consume your original loaf of bread so the result of your division is negative infinity.

Now take many infinitely thin slices to make up your original loaf of bread. You wil need all the infinitely many slices to reconstruct your loaf of bread so your result is positive infinity.

But what if your slices are not infinitely thin but zero thin. Since 0+0=0, not even infinitely many slices will give you back your bread. This is why the division by zero is a special case, breaks every number even infinity itself.

So it is axiomatically defined as error. It's effect is to cause a discontinuity in everything it touches, a singularity if you like. The division by zero is frequently used in mathematics in many calculations for example the estimation of system stability in the general sense, where the locations of such divisions are called the poles of the system.

Dividing by zero? It's common to multiply two sides of an equation by zero, but divide? Can't think of when that would be legitimate.

You can think of it as two polynomials, one dividing the other. The ratio of the two polynomials is the system output. The numerator polynomial is the forward behavior of the system, and the denomerator polynomial is the feedback behavior of the system, a memory, if you like. Each of the polynomials are linear combinations of the system input raised to various powers. This model describes every system in the universe generally. To calculate the physical poles of the system, you equate the enumerated result of the denominator polynomial to zero, i.e. you assume that you are inside a singularity of the system. You work backwards from this zero equation to find out what sort of system inputs could be capable to produce the singularity. So to answer your question in short, you don't do the division by zero but assume it then work backwards from that assumption to find the input values that can cause it.

Are you an engineer? Quite awesome how the rules of math get more involved than James Joyce.

Well I wrote it from the scientific point of view, but yes you would do the same in an engineering problem too only there your goal would be to figure out your best system parameters instead of diagnosing for the inputs.

And I agree that it is maths where you can travel beyond the limits of human imagination.

 

[SixFoot]

Try not to get too technical, but can anyone explain this in common English?
I went home and thought about it last night, but for the life of me, I can't understand why if it applies to division, it doesn't apply to the rest. What is different about division that doesn't allow that?

This was the explanation I was taught on the matter.

 

[OldLady]

Try not to get too technical, but can anyone explain this in common English?
I went home and thought about it last night, but for the life of me, I can't understand why if it applies to division, it doesn't apply to the rest. What is different about division that doesn't allow that?

This was the explanation I was taught on the matter.

Sal is my hero. Thanks.