There is no such thing as 'set of sets'. If we use the same term twice then it makes no sense - it leads to an endless regress on one side and an endless progress on the other side. The term 'set of sets' is like the terms 'the truth about a truth','knowledge about knowledge', 'facts about facts', 'method of justifying a method of creating knowledge', 'constituents of a constituent', number of numbers' etc. In all these cases if one of the terms is the primary object the other is 'knowledge' about that primery. When we have to develop knowledge about the primary object of sense then the same object has to be the source of all knowledge that we (are going to) apply to it. In this situation IF we do not want to simply describe the primery object it self (the self evident facts) instead, if we want to CREATE knowledge about it, then the only reliable method is 'statistical - empirical'. Here 'creation' of knowledge requires either prediction of future of that primery object or retrodiction of its past. In physics the physicists attempt to solve a similar problem - the are trying to find the 'constituents of a constituent' or the ultimate internal constituents of 'matter'. Russell's paradox leads to the conclusion that it is futile to try to find the ultimate internal constituents of matter if we begin with the simplifying assumption that 'matter is the ultimate constituents of matter'. Similarly acceleration is 'speed of increase in speed'. It is impossible to have an expression for 'speed of increase in speed'. 'Speed of increase or decrease in speed' must be an exponential function of which 'speed' itself is the base (like half-life time in case of natural radioactive decay). Acceleration = s^t (where s is a time-like quality). The idea of 'number of numbers' also leads to problems that are impossible to solve. We all accept that N*1/N=1. Here, if N is always a number less than 1, then, 1/N is always more than 1. When N=0, 1/N must be infinite and when N=1, 1/N also must be equal to 1. The problem is, if N*1/N=1 then there must be one to one relation between N and 1/N, that is. the number of numbers between 1 and 0 must be equal the number of numbers between 1 and infinity if N*1/N=1. In XY=1, if X is not equal to Y then for each value of X (<1)number of values of Y (corresponding to that single value of X), is infinite! What Russell's paradox reveals is the limitations of the positive communicable language (verbal or numerical) when it is used as the carrier of knowledge.
V.Gopal wrote: > <snip pseudo-scientific babble> > In XY=1, if X is not equal to Y then for each value of X (<1)number of > values of Y (corresponding to that single value of X), is infinite!
It should be easy to enlighten the rest of us with this profound observation. Let X = 1/2. Since you claim there are an infinite number of values of 'Y' which satisfy XY=1, perhaps you could give us just eight or ten of them...
-- There are two things you must never attempt to prove: the unprovable -- and the obvious. http://www.crbond.com
On Tue, 03 Sep 2002 18:50:18 +0100, V.Gopal wrote: > There is no such thing as 'set of sets'.
You've never worked in a shop, have you? I have opened boxes containing boxes on many occasions. If you think that can't be represented in set theory then you need to do back to school.
> > In XY=1, if X is not equal to Y then for each value of X (<1)number of > > values of Y (corresponding to that single value of X), is infinite!
> It should be easy to enlighten the rest of us with this profound > observation. Let X = 1/2. Since you claim there are an infinite number of > values of 'Y' which satisfy XY=1, perhaps you could give us just eight or > ten of them...
You must note the conditions and my statement: The following is the condition: XY=1, X is not equal to Y and X<1. My statement is: 'The number of values of Y is infinite'. It means the relation between X and Y is not obvious, rational or communicable. In "XY=1 and X not equal to Y", we can always imagine X to be a continuous variable and once we have imagined X to be a continuous variable we have to accept that Y also is a continuous variable; it would be wrong to say that Y is not a continuous variable. This is the reason we show hyperbola by a continuous line. But a hyperbola that is asymptotic to both the axes of coordinates is symmetrical about Y/X=1. The scale used to mark X coordinate and Y coordinate is same. Therefore the condition that makes hyperbola symmetrical about Y/X=1 is that thoughout the length of the curve WE DRAW Y/X=-1.What it means is we draw a hyperbola by assuming two conditions: XY=1 and Y/X=-1. We may call this as 'mathematical deadlock', because X and Y cannot have any value other than one or [1] in this condition. We may be able to imagine that the value of X is increasing continuously from 0 to 1 but we can never imagine how the corresponding values of Y or 1/X is changing. WHEN X REACHES 1/2 FROM 0, Y REACHES 2 FROM INFINITY AND NOT FROM 1 (please not this fact.) Out of these infinite number of numbers or values of Y between infinity and 2 how many of them actually correspond to X=1/2 we cannot know. This is the reasion why we cannot have an expression for angular acceleration (T=infinity and 1/T=0 or state of rest becomes T=1and 1/T=1 or 1 cycle per unit time) within finite time. By assigning values and calculating values (if X=1/2, Y=2) we should not forget the direction of change. In geometry sense of direction is always lost. In XY=1, even when we assume X to be a rational number Y cannot be a rational number. The truth, that is not obvious, cannot be proved or disproved by logic. And the obvious requires no proof. It means we are never required to think!
> > > In XY=1, if X is not equal to Y then for each value of X (<1)number of > > > values of Y (corresponding to that single value of X), is infinite!
> > It should be easy to enlighten the rest of us with this profound > > observation. Let X = 1/2. Since you claim there are an infinite number of > > values of 'Y' which satisfy XY=1, perhaps you could give us just eight or > > ten of them...
> You must note the conditions and my statement: The following is the > condition: XY=1, X is not equal to Y and X<1. My statement is: 'The > number of values of Y is infinite'.
I *did* note them. In fact, I quoted them directly from your previous post. Your statement *was*:"In XY=1, if X is not equal to Y then for each value of X (<1)number of values of Y (corresponding to that single value of X), is infinite!"
My request was that you enlighten us by citing eight or ten of these values taken from the infinity of those you claim are available for the specific case XY=1, X = 1/2 so that (X < 1) and X is not equal to Y. I come up with X = 2. What are some of the other values?
<snip more babble>
-- There are two things you must never attempt to prove: the unprovable -- and the obvious. http://www.crbond.com
> On Tue, 03 Sep 2002 18:50:18 +0100, V.Gopal wrote:
> > There is no such thing as 'set of sets'.
> You've never worked in a shop, have you? I have opened boxes containing > boxes on many occasions. If you think that can't be represented in set > theory then you need to do back to school.
> > You've never worked in a shop, have you? I have opened boxes containing > > boxes on many occasions. If you think that can't be represented in set > > theory then you need to do back to school.
> I don't think school would help.
Number of primery objects within a set is always in terms of units or whole numbers or integers. If we accept this fact then Russell's paradox does not exist because then we accept that we cannot arbitrarily assign any value (N) to the number of sets within the mother set (which is the set of all sets) independent of total number of primery objects within the mother set. If there are N primery objects within mother set, we cannot have more than N/2 sets within the mother set, if we want to have minimum of two primery objects within each set. There is no paradox here. If we talk of 'set of sets' independent of number of primery objects within the mother set then we reach a stage when we have to know 'number of numbers' within unit or within 'one'. We cannot know number of numbers within ONE because number of numbers within ONE must be equal to that between infinity and ONE because T*1/T=1. We can never prove that set theory is wrong by using Russell's paradox. Set theory is perfectly logical. But we can use Russell's paradox to prove that we cannot have any expression for angular acceleration or increase in frequency per cycle or rate of increase in number of CYCLES PER CYCLE. If a flywheel, initially at rest (period per cycle=infinity and frequency=1), reaches a frequency of one in one second then what is its angular acceleration? Note that increase in frequency (in whole numbers?) has to be continuous within cycle (or within 1)! This is a paradox and if we use any expression to convey the rate of change of frequency it would engender the same paradoxes that Einstein created in his Special Relativity Theory. I believe that our idea of paradox and illusion are born out of our inability to understand continuous change.
> > > You've never worked in a shop, have you? I have opened boxes containing > > > boxes on many occasions. If you think that can't be represented in set > > > theory then you need to do back to school.
> > I don't think school would help.
> Number of primery objects within a set is always in terms of units or > whole numbers or integers. If we accept this fact then Russell's > paradox does not exist because then we accept that we cannot > arbitrarily assign any value (N) to the number of sets within the > mother set (which is the set of all sets) independent of total number > of primery objects within the mother set. If there are N primery > objects within mother set, we cannot have more than N/2 sets within > the mother set, if we want to have minimum of two primery objects > within each set. There is no paradox here. If we talk of 'set of sets' > independent of number of primery objects within the mother set then we > reach a stage when we have to know 'number of numbers' within unit or > within 'one'. We cannot know number of numbers within ONE because > number of numbers within ONE must be equal to that between infinity > and ONE because T*1/T=1. > We can never prove that set theory is wrong by using Russell's > paradox. Set theory is perfectly logical. But we can use Russell's > paradox to prove that we cannot have any expression for angular > acceleration or increase in frequency per cycle or rate of increase in > number of CYCLES PER CYCLE. If a flywheel, initially at rest (period > per cycle=infinity and frequency=1), reaches a frequency of one in one > second then what is its angular acceleration? Note that increase in > frequency (in whole numbers?) has to be continuous within cycle (or > within 1)! This is a paradox and if we use any expression to convey > the rate of change of frequency it would engender the same paradoxes > that Einstein created in his Special Relativity Theory. > I believe that our idea of paradox and illusion are born out of our > inability to understand continuous change.
There is a typing mistake in my previous posting ; when period per cycle is infinity frequency should be zero and not one, by mistake I have typed one. I am sorry for the error.
Charles R. Bond wrote: > <ssnip> > I *did* note them. In fact, I quoted them directly from your previous post. Your statement *was*: > "In XY=1, if X is not equal to Y then for each value of X (<1)number of > values of Y (corresponding to that single value of X), is infinite!"
> My request was that you enlighten us by citing eight or ten of these values taken from the infinity > of those you claim are available for the specific case XY=1, X = 1/2 so that (X < 1) and X is not > equal to Y. I come up with X = 2. What are some of the other values?
> <snip more babble>
I've been waiting for an intelligent reponse to the above question, but I now realize that such a response is impossible.
Why?
Because, before you are able to derive and post a complete reponse, you must first have completed 1/2 of the total response. But before you compose 1/2 the total response, you must compose 1/2 of the 1/2 response (1/4 of the total). Before you compose this, you must have first composed 1/2 of it, ad infinitum. Therefore, there are an infinite number of steps required before you even type the first letter of your post. It follows that a response is impossible.
It also follows that that your original argument was never derived or presented and that your original post was never completed.
-- There are two things you must never attempt to prove: the unprovable -- and the obvious. http://www.crbond.com
> > <snip babble> > > I believe that our idea of paradox and illusion are born out of our > > inability to understand continuous change.
> Speak for yourself (and possibly Zeno).
Dear brother, we seem to differ at the fundamental level: You seem to believe that the unprovable must always be false and the truth must always be provable. Every incommunicable truth is unprovable. I can at least give one example of unprovable or incommunicable truth. The state of change is incommunicable and therefore existence of state of change is unprovable. No scientist seems to be convinced that 'state of change' is a reality. This is the reason why scientists replace the state of change by a series of equilibrium states. The belief that there is one value of the reciprocal of 1/2, and it is 2, cannot be proved wrong if we are not able to visualise - feel - the state of change. Deceleration represents a state of change in the following example: A fly wheel is initially rotating at 1 RPM. This is a state of equilibrium. An external force (say brake) brings it to 0 RPM. A clock shows the duration of deceleration. Numerically it means: Initially T (or period per cycle)=1 and also 1/T (frequency)=1. At the end of a finite duration, T=infinity and 1/T=0. The state of change or deceleration makes the number(s) representing 1/T(or frequency) to decrease continuously from 1 to 0 and the number(s) representing T (or the period per cycle) to increase from 1 to infinity. Here all numbers between 0 and 1 and also 1 to infinity are continuous. If you say that 1 becomes 1/2 and also 2 at the same time then does it mean that within the next 1/2 (half) 2 becomes infinity? What is the mathematical relation between T and 1/T? It is like the relation between mass and number atoms within that mass. The natural radioactive gives the continuous relation between a number and its reciprocal. In the process of natural radioactive decay mass at any instant of time is like period per cycle (T) and the number of decaying atoms is like frequency (1/T). When mass (T) becomes 1/2 what is the corresponding number of atoms (1/T) at that time? Is it 2? If number of numbers between 0 and 1 is N, then is the number of numbers between any two consicutive integers same as that between 0 and 1? (Here set theory is used, numbers are not continuous and T*1/T=1 is not true beacuse each set contains only numbers between 0 and 1) If T*1/T is true then the number of numbers betwen 0 and 1 must be equal to that between 1 and infinity (like in the case of RPM decreasing from 1 to 0). In this case the relation between number of values T and 1/T is one many. One can only create (explain?) a situation in which the unprovable is proved by the situation itself, but one cannot do anything further to make one to understand the situation itself. Those who do not understand the situation in which the unprovable is true should not conclude that the unprovable is always false.
|> |> Dear brother, we seem to differ at the fundamental level: You seem to |> believe that the unprovable must always be false and the truth must |> always be provable. ...
Given that incompatibility, do you think that we could drop this thread? It has little or nothing to do with numerical analysis.
Regards, Nick Maclaren, University of Cambridge Computing Service, New Museums Site, Pembroke Street, Cambridge CB2 3QH, England. Email: n...@cam.ac.uk Tel.: +44 1223 334761 Fax: +44 1223 334679
> > > <snip babble> > > > I believe that our idea of paradox and illusion are born out of our > > > inability to understand continuous change.
> > Speak for yourself (and possibly Zeno). > Dear brother, we seem to differ at the fundamental level: You seem to > believe > that the unprovable must always be false and the truth must always be > provable.
<snip babble>
I doubt anyone has any interest in your interpretation of my beliefs -- I certainly don't. (Besides which you are not even close!)
Stick to the topic of this thread, if you have anything to offer. Give us some of the values for Y from the infinite set associated with the value of X=1/2.
> > > > <snip babble> > > > > I believe that our idea of paradox and illusion are born out of our > > > > inability to understand continuous change.
> > > Speak for yourself (and possibly Zeno). > > Dear brother, we seem to differ at the fundamental level: You seem to > > believe > > that the unprovable must always be false and the truth must always be > > provable. > > <snip babble> > > I doubt anyone has any interest in your interpretation of my beliefs -- I certainly don't. (Besides > which you are not even close!) > Stick to the topic of this thread, if you have anything to offer. Give us some of the values for Y > from the infinite set associated with the value of X=1/2.
I had stated: if T*1/T=1. and, if T decreases continuously from 1 and, if and only if we accept that 1/T also increases CONTINUOUSLY from 1, then for each value of T, 1/T has in an finite number of values. I accept that my statement is unprovable, but at the same time I KNOW THAT MY STATEMENT IS TRUE. The integral of units of time (T) is again time T (total). But 1/T or frequency has no unit, it is the level of activity like temperature (1/T is not additive), therefore integral of 1/T (or angular acceleration) is given by the Log(T) and this logarithmic scale has to begin from T=1 (Log 1=0) AND NOT FROM ANY OTHER VALUE OF T. Moreover we cannot arbitrarily asign any balue to the base of this lagarithmic table. 1/T as the continuous function of T is incommunicable there I cannot give 'values' of 1/T corresponding to any value of T. I am sorry.
> > <ssnip> > > I *did* note them. In fact, I quoted them directly from your previous post. Your statement *was*:
> > "In XY=1, if X is not equal to Y then for each value of X (<1)number of > > values of Y (corresponding to that single value of X), is infinite!"
> > My request was that you enlighten us by citing eight or ten of these values taken from the infinity > > of those you claim are available for the specific case XY=1, X = 1/2 so that (X < 1) and X is not > > equal to Y. I come up with X = 2. What are some of the other values?
> > <snip more babble>
> I've been waiting for an intelligent reponse to the above question, but I now realize that such a > response is impossible.
> Why?
> Because, before you are able to derive and post a complete reponse, you must first have completed 1/2 of > the total response. But before you compose 1/2 the total response, you must compose 1/2 of the 1/2 > response (1/4 of the total). Before you compose this, you must have first composed 1/2 of it, ad > infinitum. Therefore, there are an infinite number of steps required before you even type the first > letter of your post. It follows that a response is impossible.
> It also follows that that your original argument was never derived or presented and that your original > post was never completed.
> On Tue, 03 Sep 2002 18:50:18 +0100, V.Gopal wrote:
> > There is no such thing as 'set of sets'.
> You've never worked in a shop, have you? I have opened boxes containing > boxes on many occasions. If you think that can't be represented in set > theory then you need to do back to school.
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