1. Generally when you see 1/0 you've made an error in your calculations. This is in the physics section because my question is... Though the undefined is undefined... Is it physically possible for a 1/0 anomaly to exist. Anywhere. 1/0 in a black hole, coming from a 4th dimension...

2. ### Related Discussions:

3. Division by zero may occur in a physical/mathematical model. Such as for example the amplitude of an undamped oscillator at resonance frequency. This is usually because the model is to simple, in the mentioned example it is because there really isn't any completely undamped systems. What will be observed is actually just an extra high amplitude. Most of the times when a division by zero occurs it can get treated as an infinity or more realistically a very large value.

Now you ask whether division by zero "exists". I think you will have to define with what you mean with the word "exists" in a physical sense in order to be able to answer that question.

4. Originally Posted by gravitywell
Generally when you see 1/0 you've made an error in your calculations. This is in the physics section because my question is... Though the undefined is undefined... Is it physically possible for a 1/0 anomaly to exist. Anywhere. 1/0 in a black hole, coming from a 4th dimension...
no

5. "...Division by zero may occur in a physical/mathematical model..."

– that is non-correct, it is possible to divide only a number by a number, when zero isn’t a number.

Zero is a concrete realization of the null set, which in a "usual" language is as (e.g.) "in this point on the number axes there are no numbers"

Cheers

6. Originally Posted by SSDZ

– that is non-correct, it is possible to divide only a number by a number, when zero isn’t a number.

Zero is a concrete realization of the null set, which in a "usual" language is as (e.g.) "in this point on the number axes there are no numbers"

Cheers
No, I don't think this is quite right. First it depends what you mean by "number" - natural, real, complex or what? It is true that some people do NOT regard zero as being a natural number, some do; this is purely a matter of taste as far as I can see.

So, to avoid a pointless controversy about whether one can "count" zero objects, stick with the reals (by talking about the "number axis" this is what you seem to mean anyway).

Zero is most certainly on the real line, and considering the reals as a set we most definitely then have that . Notice this subset is a set with exactly one member.

But the empty set (you call it the null set) is the set with NO members, so that , so I don't think your assertion about zero being the "concrete realization of the null set" is correct.

7. You can only not divide 4 / 0 but you can have a relation of 4/0 and express it like that 4/0 or 4 : 0 as we used to write on basicschool.

For instance speed you can write as 0/4 m/s but also as 4/0 s/m. Fysicwise or mathematecal there is nothing against that as a notation as long as long as you don,t try to put one number to it.
A number can be a quotential number like 4 for a speed of 4/1 m/s.

Allthough it is onenumber then that one number still expresses a relation : 4/1. Notationwise you don,t write the number one then but in fact it still is there. It,s just convention to not write it it spares ink and paper a bit also. But a number for speed is still a relation as you can,t divide meters by seconds the way you cut a measuring tape in pieces. If I have one dollar and you have nothing or vice versa it,s a relation of 1 : 0 or 1/0. I could imagine this two ways of notation would be used side by side (/) where dividing is meant or approriate and ( to express a relation as such that cannnot be divided. Another example would be a rectangle of 4:1 not 4/1 which would result in one number : 4 then you loose the idea of a rectangle in the process.

8. No. Division by zero is not possible. A/b is defined as A*b^(-1), where b^(-1) is the multiplicitive inverse of b. Now, a*0=a(1+(-1))=a-a=0. Hence, 0 has no multiplicitive inverse as the multiplicitive inverse of a real number a is the number that multiplies a to produce the idenity.

9. To: Guitarist

(1) "...It is true that some people do NOT regard zero as being a natural number, some do; this is purely a matter of taste as far as I can see..."

- To regard zero as being a natural number isn’t purely a matter of taste. If one regards zero as a full natural number he/she immediately obtains that on the natural number set the arithmetic only with 3 operations can be defined – without the division. So this set doesn’t include zero, though zero can be used in those 3 operations; but only formally - when somebody attempts to call an operation – let the multiplication by zero – using "usual" language then some semantic difficulties arise – what is "to multiply by the nothing?" and further for the operations with zero it becomes be necessary to define a special rules.

(2) "...But the empty set (you call it the null set) is the set with NO members, so that , so I don't think your assertion about zero being the "concrete realization of the null set" is correct..."

- what is a matter of taste in this case – is that one can introduce "null/ empty" set for any concrete set, so there appear an infinity of "empty sets"; but another can unite all these empty sets in the unique one, which "realizes" itself for concrete set with concrete semantics. The second version is – as for me – much more attractive, for example it turns out to be that such empty set directly corresponds to the absolutely infinite set; like as, e.g., it becomes be possible the mapping of complex plain on a infinitesimal sphere around zero. More – see http://arxiv.org/abs/1004.3712.

And - the zero isn't - any! - number...
Cheers

10. Originally Posted by SSDZ
To: Guitarist

(1) "...It is true that some people do NOT regard zero as being a natural number, some do; this is purely a matter of taste as far as I can see..."

- To regard zero as being a natural number isn’t purely a matter of taste. If one regards zero as a full natural number he/she immediately obtains that on the natural number set the arithmetic only with 3 operations can be defined – without the division. So this set doesn’t include zero, though zero can be used in those 3 operations; but only formally - when somebody attempts to call an operation – let the multiplication by zero – using "usual" language then some semantic difficulties arise – what is "to multiply by the nothing?" and further for the operations with zero it becomes be necessary to define a special rules.

(2) "...But the empty set (you call it the null set) is the set with NO members, so that , so I don't think your assertion about zero being the "concrete realization of the null set" is correct..."

- what is a matter of taste in this case – is that one can introduce "null/ empty" set for any concrete set, so there appear an infinity of "empty sets"; but another can unite all these empty sets in the unique one, which "realizes" itself for concrete set with concrete semantics. The second version is – as for me – much more attractive, for example it turns out to be that such empty set directly corresponds to the absolutely infinite set; like as, e.g., it becomes be possible the mapping of complex plain on a infinitesimal sphere around zero. More – see http://arxiv.org/abs/1004.3712.

And - the zero isn't - any! - number...
Cheers
No.

First 0 is a number. Whether you start the natual numbers with 0 or 1 is matter of semantics, but in any case 0 is a perfectly legitimate, and in fact rather necessary number.

Second. There is one and only one empty set. There is no such thiing as an "absolutely infinite set". The Arxiv paper to which you provided a link is total crap.

Third. There is no such thing as division by zero.

11. Not division but relation there is and sometimes the notition is the same. 0/1 m/s is the same as 1/0 s/m. It,s purely and merely a matter of convention to write m/s instead of s/m nothing fundamental about that. It,s simply how two meassurements, duration and distance are related to each other and to something or someone.

12. First; please use the "quote" function provided here. It's top-right of your browser box. It makes life a whole lot easier for all of us,
Originally Posted by SSDZ
the natural number set the arithmetic only with 3 operations can be defined – without the division. So this set doesn’t include zero,
Why? Zero is the additive identity. Natural numbers can be added and multiplied. Since, by definition, these are closed operations, this of course implies an identity for each operation, you can call them what you want. I call them 0 and 1, respectively. Seems a reasonable choice to me but it need not imply an inverse. In fact the natural numbers have no additive or multiplicative inverse. So what?
what is "to multiply by the nothing?"
Er...nothing? Am I close?
and further for the operations with zero it becomes be necessary to define a special rules.
No idea what you are getting at here
an infinity of "empty sets"; but another can unite all these empty sets in the unique one, which "realizes" itself for concrete set with concrete semantics.
As Rocket said, this is garbage. Look up the definition of set identity

Originally Posted by Ghrasp
Not division but relation there is and sometimes the notition is the same. 0/1 m/s is the same as 1/0 s/m.
EEEK! So 1.0 = 0.1. Yay!

13. EEEK! So 1.0 = 0.1. Yay!
Don,t panic like I pointed out you can't divide apples by pears just the same you can,t divide meters by seconds and that,s what you just did doing blind math (or you where not reading my post). You divided automatically where you can,t divide.

If I travel ten mile distance during one hour I travelled 10/1 m/h or 1/10 h/m, no physical or mathematical law telling you how to write that as it,s exactly the same.

Bolt runs 100 m per 9 seconds or 9 seconds per hundred meter it comes down to the same.

if I travel that ten mile distance in two hours I travelled 10/2 m/h not 5/1 m/h ( maybe 2*5/1 but I could not travel the same speed for the whole trajektory).

If you want an average per hour for the trajektory, being interested in that for whatever reason, you are not dividing 10/2=5 but 10/2 (miles) ánd 2/2 (hours) ; both by 2 ( and not meters by seconds) to come to a "per hour" notition. Then average speed is 5/1 m/h.
Mathematical that,s different then cutting (dividing) a measuring tape in two pieces or two oranges shared over four children.

So if bolt runs 100 meters/9 seconds or 9 seconds per 100 meters and 0 m /1 s is meaningfull then 1 s/ 0m (or 1/0 s/m) is also meaningfull.

What,s not meaningfull is dividing meters by seconds but that,s an apple / pear problem and the question was if 1/0 can be meaningfull, not the dividing on itself allthough that may be how most will read 1/0 in some cases as speed math is used in a way that you can,t read it that way or you can but you better not because you won,t understand how it is meant.

14. trajectory

Meaningful

although

notation?

15. Originally Posted by Ghrasp
Not division but relation there is and sometimes the notition is the same. 0/1 m/s is the same as 1/0 s/m. It,s purely and merely a matter of convention to write m/s instead of s/m nothing fundamental about that. It,s simply how two meassurements, duration and distance are related to each other and to something or someone.
Completely wrong.

16. Alwats interesting to know you're opinion mr Rocket..

With 0.1 or 100 the number zero doesn,t even have a meaning in that it is a necessary symbol. It only funktions in the numerical system. 0 as notation in 10, 100 or 1000 could be easily changed by another sign like @ or any other. 1@@@/1@=1@@ 1/1@@=@@1 etc. Would be little confusing at first but it won,t be to difficult to learn children to calculate and notate that way because calculationwise it is the same.

Natural numbers are regarded as either the positive numbers or the numbers that are not negative. Zero not being positive or negative.
The discussion if zero is a natural number should be about zero not being positive or negative.
The whole definition of natural numbers as only the positive (or not negative) numbers in my opinion is questionable in these days of anti-particles, anti-matter etc.

If one particle is 1 then an anti-particle logicwise would be -1 and if anti-particles anti matter etc are natural also then -1 is natural too. Then all natural numbers would be either positive ór negative except zero making it not a natural number. It would exist only as a limit +0 or -0.

In that case 1/0 would be endless, positive or negative, and in this case obviously positive as 0/1 ecquals +0/+1 so endless is what I consider it to be.

17. always
functions
equals

18. Originally Posted by Guitarist
Why? Zero is the additive identity. Natural numbers can be added and multiplied. Since, by definition, these are closed operations, this of course implies an identity for each operation, you can call them what you want. I call them 0 and 1, respectively. Seems a reasonable choice to me but it need not imply an inverse. In fact the natural numbers have no additive or multiplicative inverse. So what?
- indeed, the example with nature number set is not too good; though on this set the operation “division” can be defined also - 4:2=2; N:1=1, etc. Though that is non – essential in this case, zero isn’t any number. So you can replace “natural” by “real” and further obtain that any real number have additive or multiplicative inverse – besides zero.

and further for the operations with zero it becomes be necessary to define a special rules.No idea what you are getting at here
- "special rules" – an example: if the zero point on the number axes is "usual" number point then the interval [0,a] is more then (0,a], but an rule says that these intervals are absolutely identical. Moreover, the number a+0+0+0….- where the number of zeroes is infinite is absolutely precisely equal to a.
That is because of zero isn’t a number – as, e.g., it isn’t a number zero’s opposite partner – the infinity. Though with a correction – if any infinity isn’t a number, zero’s partner is absolute infinity – see http://arxiv.org/abs/1004.3712
, page 8.

an infinity of "empty sets"; but another can unite all these empty sets in the unique one, which "realizes" itself for concrete set with concrete semantics. As Rocket said, this is garbage. Look up the definition of set identity
(1) – let without Rocket? – he is too categorical…

(2) This point isn’t too essential – in the paper (link above) only the conception of the unique null set is used – page 6; but to relax seems be worthwhile to explain what did that mean in the context of the post Wed Jul 14, 2010 4:29 am.

So let consider some two sets, let – a set of cows in a farm and, e.g., the set of members in this forum. Each set has own empty set, and these - empty -sets are specific, since if they are identical then one can conclude that the members and the cows are identical also…

19. So let consider some two sets, let – a set of cows in a farm and, e.g., the set of members in this forum. Each set has own empty set, and these - empty -sets are specific, since if they are identical then one can conclude that the members and the cows are identical also…
I agree to that. Zero is the same as nothing in this. It means nothing if it,s not specified in relation to what. On itself it has no meaning.

But ..... you have female cows and male cows, red cows and black-white cows, female forummembers and male etc. So you would have to specify for that also for the same reason, not to categorize, then ? Because for humans and cows you can think of a category just the same as for everything (which is a category on itself).

20. The additive identity does not have a multiplicative inverse in any field. If you don't understand that sentence, you're in no position to argue the meaning of 1/0.

21. If you don't understand that sentence, you're in no position to argue the meaning of 1/0.
What meaning ? you have to specify the context where it is used.

As I mentioned you can cut/divide a measuringtape of 100 cm to 5 pieces : 100/5=20 cm each but not to zero pieces and still have centimeters.

But a trainride of 100 miles / 2 hour you can,t cut the miles with the hours. To calculate the distance per hour assumed the train travels at constant speed.
The math there is :
100/2 : 2/2. The number you use to divide does not stand for seconds even though it is the same number (which is logic as you want to know the distance travelled per hour).

And therefor 100/1 m/h is not different from 1h/100 m or Would you start to argue on that also when some tells you that a runner runs one hour per 20 miles ? That,s a fully logic (and common) type of statement showing that reversing the meters and seconds is not changing anything.

And thus 1/0 s/m does not have the problem of dividing by 0.

22. It's obvious that you don't understand that sentence. Specifying that whatever is a field is context enough. Your example of 1/0 seconds per meter is basically meaningless. The whatever isn't moving, so there's no meters to multiply by, nor seconds to divide by. Another way to look at that is as the answer to the question, "How long will it take a car to travel 1 meter if it's moving 0 m/s?" The answer is obviously that it'll never happen, so how long has no meaningful answer, not even infinity. (Even after an infinite amount of time, the car isn't going to suddenly jump forward a meter.)

23. Your example of 1/0 seconds per meter is basically meaningless. The whatever isn't moving
eheh, seconds is considered a distance in four dimensional fysics so there is still movement (time). Just no distance in meters. Hence : 0m/1s or 1s/0m = 1/0 s/m
(or 1s : 1m to distinguish from dividing to pieces)

24. from a comic strip I like...

"1/0" is a paradox; in a way that "0/1" is not. Nothing can be divided by zero. If one approaches the formula from the positive side, it would appear that the answer is an infinite positive value. If one approaches the formula from the negative side, the opposite is true. Thus, anything divided by zero is simultaneously positive and negative infinity. "One over Zero" is a paradox in another way too, in a way that transcends mere arithmetic. One is something, and Zero is nothing. The fact that the universe holds something over nothing, that it prefers to exist, rather than not exist, is fundamentally absurd. No being can ever come to deserve its own birth. 1/0 is a cry out against mere logic and efficiency. Stuff exists. All existence, all truth, cannot be ultimately justified: it can only be described, explained, and enjoyed.

25. Zero (0) being nothing leaving it away should make no difference :
1/0=1/= 1 then ?

But with every number without being specified it is positive: 2=+2, 3=+3 etc.
Therefor 0=+0 ? 0 (+0) can be real then but not as a defined number but more as limit because it is +0 or -0. And then 1/0 =1/+0=endless. The added + is just left away but that,s common usage.
Otherwise 0 is not specified as being negative ór positive as all other numbers always are.

26. Originally Posted by SSDZ
zero isn’t any number. So you can replace “natural” by “real” and further obtain that any real number have additive or multiplicative inverse – besides zero.
well I am glad to see you have at found the quote button. But I don't understand what you mean. The reals most certainly have an additive inverse for each and every one of its members, including zero, but they don't have a well-defined multiplicative inverse for zero, as our resident magician told you.

The proof is not hard, I think - just use the cancellation law (but I doubt you will try)
- "special rules" – an example: if the zero point on the number axes is "usual" number point then the interval [0,a] is more then (0,a],
This is baffling. The sets have exactly the same number of elements - this is because each of these sets is uncountable.
zero’s opposite partner – the infinity.
Err....pardon?

So let consider some two sets, let – a set of cows in a farm and, e.g., the set of members in this forum. Each set has own empty set, and these - empty -sets are specific, since if they are identical then one can conclude that the members and the cows are identical also…
Check your logic here, the conclusion does not follow from the premises. Each set does NOT have its own empty set. Look up the definition of set identity, I cannot be bothered to give it to you, as you seem uninterested in learning.

27. Ghrap: Your posts are such nonsense, they are "not even wrong", to quote a famous physicist.

Please stop posting such rubbish, there may well be those out there who think they might learn something by visiting this site, God help them

28. Originally Posted by Ghrasp
Your example of 1/0 seconds per meter is basically meaningless. The whatever isn't moving
eheh, seconds is considered a distance in four dimensional fysics so there is still movement (time). Just no distance in meters. Hence : 0m/1s or 1s/0m = 1/0 s/m
(or 1s : 1m to distinguish from dividing to pieces)
If you want to invoke 4-dimensional movement, you can't just do it partially. In any case where you try to ask how long does it take something going 0 to get somewhere, the answer is that the question doesn't make sense. In 2+ dimensions, you can ask the slightly different question of when will this thing moving in the wrong direction reach this point, which has the same answer for a slightly different reason.

29. In any case where you try to ask how long does it take something going 0 to get somewhere, the answer is that the question doesn't make sense.
I wasn,t asking that. Someone could ask what the speed for a period of time of a train is standing on a railroad with no fuell : nill meter for an hour for example or in math 0m/h. Asking for the speed during a period of time is asking how much something travelled in meters during a specific period of time. That distance can be zero as in this example.
Sixty minutes no movement : 60 min /0 m or 60/0 Min/m. If the hour before and after it was 100 miles/hour you can calculate an average speed for a trajektory of 200 miles or in this case 3 hour (and normally 2). No problem whatsoever doing that math using 1/0 h/m.

But even if I would ask that question it,s not that a strange question it just depends who I ask. If you sit still you,re only without movement (at least obvious) for others that sit still, a selective group, the floor etc but not for someone walking by during that period. Rest is just as relative as speed is.

Or someone on the station could make a phonecall with someone on the train : How much more seconds/hours will it take before the train starts riding again.

30. None of the meaningful questions you bring up have the answer 1/0. Taking the inverse gives an answer to a different question, and for questions with an answer of 0, the inverse question is as meaningless as 1/0.

31. Originally Posted by Ghrasp
Alwats interesting to know you're opinion mr Rocket..

With 0.1 or 100 the number zero doesn,t even have a meaning in that it is a necessary symbol. It only funktions in the numerical system. 0 as notation in 10, 100 or 1000 could be easily changed by another sign like @ or any other. 1@@@/1@=1@@ 1/1@@=@@1 etc. Would be little confusing at first but it won,t be to difficult to learn children to calculate and notate that way because calculationwise it is the same.

Natural numbers are regarded as either the positive numbers or the numbers that are not negative. Zero not being positive or negative.
The discussion if zero is a natural number should be about zero not being positive or negative.
The whole definition of natural numbers as only the positive (or not negative) numbers in my opinion is questionable in these days of anti-particles, anti-matter etc.

If one particle is 1 then an anti-particle logicwise would be -1 and if anti-particles anti matter etc are natural also then -1 is natural too. Then all natural numbers would be either positive ór negative except zero making it not a natural number. It would exist only as a limit +0 or -0.

In that case 1/0 would be endless, positive or negative, and in this case obviously positive as 0/1 ecquals +0/+1 so endless is what I consider it to be.
Utter rubbish, as usual.

The existence of natural numbers has absolutely nothing to do with elementary particle physics, or physics at all.

32. None of the meaningful questions you bring up have the answer 1/0. Taking the inverse gives an answer to a different question, and for questions with an answer of 0, the inverse question is as meaningless as 1/0.
written reversed for specific situation 9m/3s ecquals 3s/9m (Bolt and other examples people running seconds per meters distance in a match) it,s just written reversed but the athletes run the distance in meters per amount of measured seconds just as wellnota significant difference but when the distance is set at forehand s/m mostly has a preference and with a world hour record m/h has a preference.

33. Originally Posted by Guitarist
Originally Posted by SSDZ
zero isn’t any number. So you can replace “natural” by “real” and further obtain that any real number have additive or multiplicative inverse – besides zero.
well I am glad to see you have at found the quote button. But I don't understand what you mean. The reals most certainly have an additive inverse for each and every one of its members, including zero, but they don't have a well-defined multiplicative inverse for zero, as our resident magician told you.
The proof is not hard, I think - just use the cancellation law (but I doubt you will try)
- sorry for my not too correct answer – I mechanically copied your “additive or multiplicative inverse”. The reals indeed “most certainly have an additive inverse”. But as to “they don't have a well-defined multiplicative inverse for zero” – that is too polite, more correct – as to me – is “have non-defined multiplicative inverse for zero”.

-
- "special rules" – an example: if the zero point on the number axes is "usual" number point then the interval [0,a] is more then (0,a],
This is baffling. The sets have exactly the same number of elements - this is because each of these sets is uncountable.
- agree, the example is non- correct, one should deal with the infinities more cautiously. But again about “special rules” – that also means that in any arithmetic the notion “0” is introduced by a special way – i.e. – by the special definition.

zero’s opposite partner – the infinity.
Err....pardon?
- sorry, English is not my native language and sometimes I don’t understand some too native expressions – as this. But if there is a necessity to clear additionally what is "zero’s opposite partner – the infinity" in the context of post Thu Jul 15, 2010 3:12 am – it’s simple – 0 is the lim of inverse infinity.
And – your quotation is non-correctly truncated – it should be as "That is because of zero isn’t a number – as, e.g., it isn’t a number zero’s opposite partner – the infinity. Though with a correction – if any infinity isn’t a number, zero’s partner is absolute infinity"

So let consider some two sets, let – a set of cows in a farm and, e.g., the set of members in this forum. Each set has own empty set, and these - empty -sets are specific, since if they are identical then one can conclude that the members and the cows are identical also…
Check your logic here, the conclusion does not follow from the premises. Each set does NOT have its own empty set. Look up the definition of set identity, I cannot be bothered to give it to you, as you seem uninterested in learning.
-- the quotation is again truncated. The original text contains also "...but to relax seems be worthwhile to explain" – the section was a joke in some sense. But every joke should contain some truth and it is so in this case. As a sequel of the example with "members and cows" sets let consider a few expressions:
n[caws] +0[caws] = n[caws] (1)
m[members]+0[members]=m[members] (2)
and
m[members]+0[caws] =m[members] (3)

For a physicist Eq.(3) is an absurd – all dimensionalities in a formulae must be consistent. But the result (3) is correct; as it is possible since zero isn’t a number…

In a summary. The reason why I take part in this thread is to info that it is rigorously proven the existence of the absolutely infinite set "Information" – when in standard set theories such a set is impossible – and to activate some discussion - how such a set can be constructed, including that can be of an interest for some mathematicians.

When the authors of http://arxiv.org/abs/0812.2819 and http://arxiv.org/abs/1004.3712 are physicists.
And for me more interesting was "What’s so special about light?" thread, where Janus so good work made...

Cheers

34. Originally Posted by SSDZ
n[caws] +0[caws] = n[caws] (1)
m[members]+0[members]=m[members] (2)
and
m[members]+0[caws] =m[members] (3)

For a physicist Eq.(3) is an absurd – all dimensionalities in a formulae must be consistent. But the result (3) is correct; as it is possible since zero isn’t a number…
Just for interest; how does a "physicist" tell the difference between no cows and no members?

35. Originally Posted by Ghrasp
This is the fysics forum lets take the funktion F=M*a So M=F/a.
This transformation of the equation is only meaningful if a is not 0. Otherwise you have some mass that isn't accelerating, so there's no force. If you're trying to use M=F/a, you should know the force and acceleration and would be trying to work out the mass, which will fail if there is no acceleration. (In this case you'd actually have 0/0, and mass could be anything.)

Consider this:
- Let
- Then
-
-
-
-

Do you see the problem there?

36. 1/0 is meaningless,but lim (1/x) = +∞
x→0
Any funktion is only meaningfull related with some geometry to show it and every part of it being meaningfull on itself also including loose numbers.
Math can reperesent many things for a paricular use of the math.
But that,s not what I mean with meaning or showing. Then the geometry represents also like a cm in a graph representing an amount of cows.

An x and y the funktion is allready meant in relation to some sort of an x-y axis system with distances, lengths, a point (0,0) and rectangles.
It could be a checkerboard with any given length for a unit and some defined point for (0,0).
Then (1,0) is a point with a distance from (0,0). The whole of math geometry included is still not repreenting anything outside the math but within itself between algebra and geometry there is representation necessary to make the funktion in algebraic notation meaningfull. In England 1 can be an inch while creating the axs system and in europe with cm,s if the geometry really has a scale 1:1 the algebra represents in relation to geometry and the geometry shows more direkt, an inch being an inch as distance between points or length.

Assumed a checkerboard with one corner (0,0).
1 in a funktion in two dimensions can be the distance or length according to the length of one side of a square.

For example F(x)=X+1....Y is a point at ditance x from zero with one unit length added.

That distance in the geometry (direktly visible by the checkerboard) is represented in the algebra by the number 1 and therefor in relation with the geometry the number has meaning. For example for teaching.

But in this funktion 1 can,t be a length or defining a distance
(with only one point and point (0,0) implied as reference for it automatically a distance or length is produced as result )

Because F(x)*y=1 1 is always the produkt of F(x) and x or actually these points in reltionship to (0,0) as defining lengths/distance.

So 1 in this funktion can be any rectangle or area with a value same as a square on the checkerboard and (0,0) as one of it,s corners.

And you can divide an area with lines but not into line like into pieces of it.
The amount of pieces is twice as high with 1 dividing line. Only when sharing a piza thea amount of lines is the same as the amount of pieces. But a line or cut is not a piece, with slicing a bread there is always 1 more piece then cuts.

Mathematical using cuts as dividing number with a piza it would be 1/3=0,33 (per piece, in fact the same funktion as F(x)=1/x just different meaning for x and y).
Same as using the amount of pieces as dividing number : 1/3=0,33

With a bread it would be : 1/3=4 for dividing by or with cuts.
Using the amount of cuts as a dividing number (in a different mathematical convention) for a good result you would have to add one piece. : 1/3=3+1 or F(x)=1/x+1. With the bread this fits perfectly for x is zero cuts and f(x)=y, The produkt of X and Y Y*X=(1+x)=1 meaning one length of bread.

37. can you show proof (as we find it amazing, unknown)
----------

38. Originally Posted by Guitarist
Originally Posted by SSDZ
n[caws] +0[caws] = n[caws] (1)
m[members]+0[members]=m[members] (2)
and
m[members]+0[caws] =m[members] (3)

For a physicist Eq.(3) is an absurd – all dimensionalities in a formulae must be consistent. But the result (3) is correct; as it is possible since zero isn’t a number…
Just for interest; how does a "physicist" tell the difference between no cows and no members?
- that is too hard question for a physicist, I can only say that a physicist very don’t like to compare quantities having different dimensionalities. And it seems that a farmer the difference between "no cows" and "no a forum members" can explain much better…

So it is rather possible that we understood that zero isn’t a number, it is a realization of the null set for numbers case – let as "empty set for numbers set" - with a semantic something as "there aren’t any number". And it isn’t on the number’s axes, i.e. – among numbers; as, for example, seems nobody found till now an empty set for a set of cows among cows.

So a problem arises – where is it?
But this problem isn’t specific only for empty sets. For example - any point in somebody’s head contains true information as, e.g. – "in this point there isn’t of Andromeda nebula", or, e.g., - "in this bed there isn’t of Kaiane Aldorino". At that when an electron comes into Andromeda nebula – the information in the point becomes be changed instantly to remain be true; as well as any Kaiane Aldorino thought instantly become be known, though the thoughts are the members of non- material set, i.e. – of the Consciousness set.
And the same problem arises - where this information "is written"? (Here we don’t touch a problem – "Haw can one read such information?". Though it isn’t impossible that sometime somebody will overcome this problem-?)

The answer is – "somewhere in the set "Information"". And we can also conclude that the zero inverse isn’t "absolutely non- defined" – the results should be in the set "Information" also; when this set is defined in certain sense and is cognizable by mathematics, cybernetics, linguistics, synergetics, etc. – all these sciences are, in fact, the "theories of information".

So it seems we have a rather [understandable] idyllic picture.

But here a Buddhist appears and say: Yeah, zero and infinity aren’t numbers and they are tightly connected. But they aren’t totally symmetrical - e.g., when for an infinity all 4 operations are defined, for the zero so are only 3. Then one can think that zero is "more free" (or "more uncertain") and so – more fundamental, when you cannot prove the uniqueness of the Set - Shunia/ Emptiness is the first!…

Cheers

39. Originally Posted by SSDZ
Just for interest; how does a "physicist" tell the difference between no cows and no members?
- that is too hard question for a physicist, I can only say that a physicist very don’t like to compare quantities having different dimensionalities. And it seems that a farmer the difference between "no cows" and "no a forum members" can explain much better…
OK, I see your problem. It is common one and as this is a Physics forum, not Math, and as you seem to be polite, let me try and guide you.

Suppose we have a field (in the sense of a farmer) with no cows in it, also suppose we have a room with no people in it. You seem to be saying that the empty field and the empty room are somehow different. Well they are, but it is irrelevant

Or, to put it another way: Suppose we have a box labelled "apples", full of apples, and suppose we have a box of oranges labelled "oranges". Let's now tip out the contents of each of these boxes, and we are left with two empty boxes, one labelled "apples" and the other labelled "oranges"

This is a misunderstanding of elementary set theory; there are no "boxes", and no labels that can be applied other than to what is contained in the set. I could take you through it if you want, but this is not the place, and besides, I don't have the time. Suffice it to say that "empty set" means just that - all empty sets are completely identical; they contain no members.

So it is rather possible that we understood that zero isn’t a number,
If by number you a real number, then, oh yes it is, by definition.
it {zero} is a realization of the null set for numbers case – let as "empty set for numbers set"
I told you before this is false, and tried to explain why. Re-read my post

Ahhh... Having now read to the end of yours, something is badly wrong here. Any mention of "consciousness" and "Buddhist" seems badly out of place in the Physics forum, at least to my blinkered way of thinking

40. With the thing of a set of no cows it,s not about a set of anti-cows defining the set but about all
- thinkable or real - situations where you could possibly use "no cows" or where it is used.
Like the percentage of farmers in a district that have cows and the other farmers have no cows. The farmers without cows are a no cows set then, A set of farmers and not a set of anti-cows. The set of cows in this case is the set of farmers with cows.
You could make infinite amount of such sets and from that a set of "no cow" sets.
From the use the term no cow sets is meaningfull without a definition of such a set.

With an x,y system
x=2 is technically not a point but a line parallel to the y-axes with distance from Y (x=0) being 2.

Drawing two lines x=2, Y=0,5 parallel to the axes what you do is construkt a rectangle following x*y=2. That rectangle is the produkt if you draw both lines simultaneous from the axes (real or imaginative first) and stop when they cross at (2, 0,5).

That,s X*Y=1 with 1 being the produkt 1^2 or 0,5*2 etc.
As long as X*Y is a constant value every construkted rectangle follows the funktion. But allthough having the same value every produkt (thus 1) is different for every value of x. It just not shows from the number itself.

Another way of construkting the geometry could be with a calliper (or a ruler used as a calliper).
Putting the legs at a unity distance or an other distance, the needle at any point then defined as (0,0) marking a second point (1,0) and rotate the calliper ninety degree to point (0,1). That way puting out an x-y system is not necessary. Three points and a rectangular triangle with sides 1,1 and rt. 2 in length and 1 is defined as 1*1.

To construkt the funktion for x=1 another possibility is to mirror the triangle to the diagonal with a square as result and 1,1 and 1*1 is construkted or pull a line y=1 to (1,1).
The mirroring of the triangle only works for x=y=1 and 1 is thereby defined as 1*1. But how could x=2 or 0,5 fit to 1*1 in the same funktion ? As value yes but the relations are different.
Wwith the calliper idea y is mirrored from x you always get an y that is a reflection (or funktion) from x,= 1 or a multiplication of 1 or part of 1 and these values for x are multiplications of pieces of x=1.

a multiplication or it,s opposite is not the same as a produkt in the sense of a rectangle being a produkt of two perpendicular lines. In a multiplication there is no perpendicular angle and not an added dimension..
1,2*1 as multiplication can be written also as 1+0,2 a rectangle 1,2*1 not or at least it doesn,t make much sense.

41. Originally Posted by MagiMaster
-
-
-

Do you see the problem there?
which is undefined for all x

42. Well, yes, but I was hoping Ghrasp or SSDZ would figure it out.

To all lurkers, accept that division by 0 is not a mystery to mathematicians. By undefined, we mean its definition is that it has no meaning, not that it's an unknown. Trying to define it breaks lots of other things, or generally causes consequences beyond just giving an answer to 1/0. Mathematicians have studied this for a long time.

43. Consider this:
- Let a = b
- Then a^2 = ab
- a^2 + a^2 = ab + a^2
- 2a^2 -2ab = ab + a^2 - 2ab
- 2(a^2 - ab) = 1(a^2 - ab)
- 2 = 1

Do you see the problem there?
I would ask myself if it is only meant as same value for a and b or also same direktion or perpendicular ? same direktion (angularity is zero) is not explicit here so I have no idea what the angularity is and what this is about. Maybe you meant it as zero angle but how should I know ? Many cases where for A^2 there is a distinctive perpendicular opposition between both A's, many cases not. And if the geometry makes it clear It,s clear but there is also no geometry given no context whatsoever. You would have to specify at least that as additional information.

Like a=b (A=0) or a=b (A=90,) and even for a^2 it has to be clear what the angularity is between a and a because if for a=b a and b are just values then for the next a you introduce with a logic step I would like to know the angle, If a is a value of length the direction for the other a is not specified I would have to guess.

Example :

If in this case a=b as ecqual value for length at sea (meters or seamiles) but a and b east and south as direktion ( not opposed as a=-b but perpendicular opposed at sea).

{Then a^2=ab} as value may be right and true but at the same time a serious misinterpretation.

44. Originally Posted by Guitarist
Ahhh... Having now read to the end of yours, something is badly wrong here. Any mention of "consciousness" and "Buddhist" seems badly out of place in the Physics forum, at least to my blinkered way of thinking
"..."Buddhist" seems badly out of place in the Physics..."

- It is rather probable that, for example, Gell-Mann didn’t think so -?

But the point that was touched in this passage in SSDZ post of Mon Jul 19, 2010 3:53 am is something as follows. So from previous posts seems that [any] empty set of any set is somewhere in the "Information" Set also, but is outside of this set. The empty set is something as a negation and so, for example "empty set" for the set having only one member, e.g., – Andromeda nebula - is written as the statement "here is no Andromeda nebula" everywhere in the set "Information" outside the nebula (inside the nebula the statement becomes be false); including – in any point of whole Space in our Universe.

And any change in Andromeda nebula immediately is accompanied by the change in the informational content of the "empty set statement" in every point [in Space]

(Besides – an offtopic here – e.g., the fact, when informational exchange between components of an entangled couple processes instantly, isn’t too strange. For the set "Information" that is usual thing).

But so "a Buddhist" has a right to state that null/ empty set for the Set "Information" should be also outside the Set; somewhere in something that is external to the Set at that - it should contain the Set. So this External is more fundamental then the Set – we remember that we principally cannot go out from the Set to prove its uniqueness.

But such a conclusion isn’t true – the null set is inside of the set "Information" since its semantic is expressible by using any language.
Why is that so? – this problem requires of corresponding additional study.

Here we can only point out on some difference between any concrete empty set [for concrete set] and the null set. Any concrete empty set is always a "fixed" information in certain sense. Though it can change – as in the case of Andromeda nebula set’s empty set above such a changes only relate to corresponding changes in the nebula structure and, in principle, can be stable if the structure is stable.
The null set is fundamentally "non-stable", it is the infinite cyclic statement "there is no anything besides the information that there is no anything besides the information that….."

It seems that the set of SSDZ posts in this thread, that are some introduction/ comments to the paper http://arxiv.org/abs/1004.3712, is now sufficient to read and understand the paper -?

(To see the comments to the paper http://arxiv.org/abs/0812.2819 see the thread "What’s so special about light?" in this forum.

Cheers

45. Here we can only point out on some difference between any concrete empty set [for concrete set] and the null set. Any concrete empty set is always a "fixed" information in certain sense.
But is a nil-set not related to that concreteness or fixation then ?

I can formulate a positive set for the moon as the days the moon is visible or another one based on planets that have a moon. In this cases the nil-moonset is in fact a set of days or planets.

46. Originally Posted by Ghrasp
Consider this:
- Let a = b
- Then a^2 = ab
- a^2 + a^2 = ab + a^2
- 2a^2 -2ab = ab + a^2 - 2ab
- 2(a^2 - ab) = 1(a^2 - ab)
- 2 = 1

Do you see the problem there?
I would ask myself if it is only meant as same value for a and b or also same direktion or perpendicular ? same direktion (angularity is zero) is not explicit here so I have no idea what the angularity is and what this is about. Maybe you meant it as zero angle but how should I know ? Many cases where for A^2 there is a distinctive perpendicular opposition between both A's, many cases not. And if the geometry makes it clear It,s clear but there is also no geometry given no context whatsoever. You would have to specify at least that as additional information.

Like a=b (A=0) or a=b (A=90,) and even for a^2 it has to be clear what the angularity is between a and a because if for a=b a and b are just values then for the next a you introduce with a logic step I would like to know the angle, If a is a value of length the direction for the other a is not specified I would have to guess.

Example :

If in this case a=b as ecqual value for length at sea (meters or seamiles) but a and b east and south as direktion ( not opposed as a=-b but perpendicular opposed at sea).

{Then a^2=ab} as value may be right and true but at the same time a serious misinterpretation.
If a = 10 miles east, and b = 10 miles south, then a does not equal b. This remains true for any number of dimensions of Euclidean space or any other space or anything else that can be classified as a field.

47. when it's about an euclidian space we could change a and b to x and y then.
If a=b means same value but perpendicular to each other

Then with X^2 = X*Y (?) what do we have ? A line with same value as a rectangle ? meters same as meter squared and if not the same the line would be longer or shorter then the rectangle or the rectangle having more or less surface area compared with the line ? Offcourse this question allready is absurd.

and X^2 as length would also be a multiplication of two endless lines x = a with same distance to the y axis and therefor the same lines.

X=a is alaways an endless line in a euclidian system parallel to y-axis and not the distance between that line and the y axis. Allthough it is often understood that way but that is what you do and how you meaasure out the line with a ruler or something but not the line itself.

What would it turn into then multyplying x=a with x=a,(or x=0 with the y axis (x=0)) ? How would that reflect in euclidian geometry it goes beyond my imagination.

48. Originally Posted by Ghrasp
when it's about an euclidian space we could change a and b to x and y then.
If a=b means same value but perpendicular to each other

Then with X^2 = X*Y (?) what do we have ? A line with same value as a rectangle ? meters same as meter squared and if not the same the line would be longer or shorter then the rectangle or the rectangle having more or less surface area compared with the line ? Offcourse this question allready is absurd.

and X^2 as length would also be a multiplication of two endless lines x = a with same distance to the y axis and therefor the same lines.

X=a is alaways an endless line in a euclidian system parallel to y-axis and not the distance between that line and the y axis. Allthough it is often understood that way but that is what you do and how you meaasure out the line with a ruler or something but not the line itself.

What would it turn into then multyplying x=a with x=a,(or x=0 with the y axis (x=0)) ? How would that reflect in euclidian geometry it goes beyond my imagination.
but and that is quintessential to this.

49. If you interpret this

R Let a = b
S Then a^2 = ab
T a^2 + a^2 = ab + a^2
U 2a^2 -2ab = ab + a^2 - 2ab
V 2(a^2 - ab) = 1(a^2 - ab)
W 2 = 1
like that.

You get other problems that show in geometry (not in algebra, numbers and signs)

Vectorial would mean for S that drawing first step brings to coordinate (a,a) left side ecquation (a^2) and coordinate (a,b) rightside of ecquation (ab).

As you point it out, in this interpretation a ne to b (same value but different direction) the above allready goes wrong between R and S.

Also how would you know if it is meant vectoriel in this case ? We can,t even read from it if it,s one or two dimensional. It can be meant for 2-D but can be read (and thereby interpreted) as 1 D also or even mixed up. Are a and b orthogonal to each other ? Then how about A^2 ? That would be 1 dimensional then as well.

50. You're very confused. (a, a) is in no way equal to a^2. In fact, multiplication isn't defined in plain Euclidean vectors, but fortunately for this discussion, the complex multiple does and works on the same coordinates. In which case, (a, a)=a + ia, which does not equal a^2 = a^2 + i0.

If a = b, that means everything there is to know about both variables is equal, not just their magnitudes.

51. Dividing by zero is like taking and then dividing it by rice pudding.

Look I did some Tex!

52. Just take some pudding, make a whole in it and you,ll hava a zero-pudding (or pudding-zero ). You can bring it to the birthday of you,re math teacher. If you want you can apply conversion M->E to it and discover the difference for C^2 before and after.

If you meassure a distance from a wall it,s how you meassure : 1/0 m
the wall is at 0 m and what you meassure the distance for is at 1 m coordinate.

You meaasure a distance by determining coordinates as one to zero.

53. ...

Stop eating so much Rice Pudding.

54. Originally Posted by Ghrasp
Just take some pudding, make a whole in it and you,ll hava a zero-pudding (or pudding-zero ). You can bring it to the birthday of you,re math teacher. If you want you can apply conversion M->E to it and discover the difference for C^2 before and after.

If you meassure a distance from a wall it,s how you meassure : 1/0 m
the wall is at 0 m and what you meassure the distance for is at 1 m coordinate.

You meaasure a distance by determining coordinates as one to zero.
That's subtraction, not division. 1-0 is well defined.

55. Now a next little upgrade of the informational model in physics appeared, see
[0707.4657] The Informational Conception and Basic Physics , v3, (“The Informational Conception and Basic Physics”)

Tough to understand the model remains be rather desirable to read
[1004.3712] The information as absolute , (“The Information as Absolute”)

and
[1110.0003] Space and Time , (“Space and Time”)

as well as this thread, the posting “SSDZ – Guitarist ”

before/ also.

Cheers

56. I thought in physics you can never have true zero. So 1/0 is nonsense. 0/0 would be 1,-1, right? If you compare the closest to 0 with another closest to 0, the answer would be around that? Or am i blurting out nonsense now?

57. is generally indeterminate.

So, one could speculate equals all real numbers, but of course, that doesn't work out so well mathematically.

We can see this better in the context of limits where a certain input might result in a 0/0, but the function actually approaches a defined, finite limit, which otherwise can't be calculated using the substitution technique (requiring L'Hopital's Rule).

58. It's not only nonsense...but it is very old nonsense.
closed

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