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Eh? Point out where I said that infinity is best used as a verb? I corrected you once on that. I said not to use it at all, as is perfectly possible. So you're not going to explain why it is 'the result of an interative process' then? REP: The problem was there.The problem was removed by creating derivative rules.Please understand that use of "Limit" framework comes to save it. Anyways , You are not asking me right questions... i MEAN IF I CLAIM TO PROVE SOMETHING THEN THE AUDIENCE SHOULD RAISE SERIOUS DOUBTS ON IT. Doubts which comes from logical inconsistency of the my claim. We play logical game in which only the best survives. Now coming back to the Infinity. Lets understand that Real Number Set consists of all Numbers except Infinity.Which means Infinity as a concept is acceptable to MATHS.. and by excluding Infinity Maths is simply playing a TRICK of pure nonsense.How can it exclude anything which it itself doesnt understand.... So sorry but this is a fact which Maths has been trying to avoid. Now coming to Limits. Maths serves some purpose therefore it exists ... When applied to the real world .. all mathematical constructs must and must map to the applied field. Therefore the limit actually exists in Principle for all purposes. How much energy can you take out from Bucket to bring it to some absolute Value? Think about it and then reply. ======================================================= Your premise about what maths 'ought to be' is fine, for you I suppose. The rest of the world doesn't seem to agree, and I see no compelling arguments to accept your ideas. REP: Thats your choice .. I dont care whether you accept it or not. For me Christ remains more important than any thing in this world. ================================================================= So how about posting in speculations if you're not going to respect what this forum is (mathematics). REP: Listen .. I do not post anymore at http://www.scienceagogo.com.... I love them and they love me too. But there is something called as free and fair discussion..They dont believe in it.How can I share my thoughts with them? ====================================================================== And what about other considerations? does 1/3 now have a decimal expansion? it can't in your system. limits do not exist, this means there are no numbers like pi, or e, or even the square root of two (all non-rational real numbers are limits of rational ones, that is how they are defined, so you can't have them). REP: Replied above.... A GROUP can not hold Absolute Values...

No, we shall not say this. the set of natural numbers is infinite. Any finite set of numbers has a greatest elemen, what is yours? You're talking nonsense, and confusing 'real life' with maths. sure we're only ever going to use a finite number of numbers, but that doesn't mean you can declare the set of all possible numbers to be finite. they aren't a concrete set of things you're going to stub your toe on, they are a concept, an idea, and they are an infinite set. REP: Now the problem is clear .. you have declared Maths as having properties True to itself to such an extent that any thing within it may or may not relate to the real world.. thats an age old concept. Remember I had asked you a question : How many observers will it take to create the Maths...? The answer is minimum 2.Anything less and your Maths will have a good chance of never getting realized. Put up your arguments against what I have said .. we will discuss it out in case of any doubts. Secondly having an Idea of Infinite is fine with you.. and I am saying that Infinite as an Idea is irrelevant for the existence of Universe and therefore Maths should also express the same. If it is not the case then we know Maths is terribly wrong somewhere. I can give you hints but before that I would like to hear some honest confessions on the incompleteness of its framework.What all current Maths can not perform? and why? The complexity of Maths makes it appear as if every now and then Nature is nothing but just a Manifestation of Maths.. Thats stupid. Let me tell even the Mathematical Random Numbers are not perfect answer to the Nature's way of choosing things. Visit http://www.scienceagogo.com and read Anomaly in Randomness. ======================================================================================== you ain't going to convince anyone otherwise, not least if you keep asserting that 'infinity is the result of an iterative process' which no one else appears to have done, and no one understands. REP:I guess it was you who wanted to use it as a verb.. not me. I was never in favour of it .. in any way. =========================================================================================== when i said i can't offer a simple definition of infinity and that i suspect there might not be such a thing i was strictly refering to the real world around us. there are certainly infinite sets in maths, infinite cardinals, sums from one to infinity, points at infinity. REP:Yes I have good sympathy for those who wish to use Infinity to solve there computational problems. Simply because something is not true doesnt mean it looses its applicability.It helps to keep the Maths simple whereever required.I dont deny its use. But saying that Mathematically Infinity has any meaning is incorrect. Thus the use of Infinity is at best an approximation used to model a more generalized Framework of logic and reasoning. Hope it is clear. Talk to modern Mathematicians and they will give you reasons why common sense appears to have an upper edge over resource crazy Mathematical Answers. And yes there was a question : why to change Maths? Well the reasons are simple... any further applicability requires good amount of rework in some areas.Including understanding of Group Theory and Number Theory.

what on earth is an interative process? if you don't define your terms properly they cannot be 'disproven' or 'proven'. they just make no sense. REP:I meant iterative process. ========================================================== i will not even attempt to disprove that since I do not think 'infinity is an interative process', nor do i think its negation is true since i have no idea what that even means. REP:So sorry for the misunderstanding..keyboard mitake.. ========================================================== point out one person that has said infinity is an interative process. or a process fullstop. REP:The term was taken too seriously. ========================================================== i can tell you how infinity is used in maths (many ways) and i will keep repeating that it is merely a short hand to indicate 'not finite' in different ways, and any statement involving the word can almost certainly be rewritten to omit the word entirely. i can't offer a simple 'definition' of what infinity 'is', since i don't necessarily think there is one, or needs to be one *for mathematics*. REP: Good Thought.Maths has no infinity. In fact thats what I am also saying.But I would like this to be taught in Maths. That there is no Maths with Infinity.Lets call the Real Number Set Finite. So if we ask how many Numbers are there in the Real Set ? We say there are Finitely Realizable Number points. Hope you realize the consequences of it. The Flat Pitch of Number Theory Becomes Curved. ==========================================================

Universe: All known and unknown matter, anti-matter, and empty space that has ever existed in any time period known, and will be known. REP: The unknown I am talking about has to no qualification. ================================================ It is what exsist in the present, past, and what will exsist. Just because we don't know it exsist, then that doesn't mean it isn't their. REP: If you have read carefully ,I am saying everything exists and at the sme time Nothing(absolutely nothing) exists.The Unknown part always remains as unknown.Which can not be communicated using any means. ============================================== If it does not exsist and you don't know it does or not it can't be in the Universe. If it does exsist and we don't know this, it is still in the Universe. REP:Go through the discussion on Nothing.

You are contradicting your own statements... If by 'we' you mean the general public and the belief that somehow mathematical things are 'real' then they don't. REP: Well I say the entire Mathematics comes out of Subjective Reasoning. Somewhere in the complexity of problems we like to think that we are inventing a pure Mathematical Approach when we are simply trying to model the actual Real World. The incompleteness comes as a consequence of partially correct assumptions, the rest as we know becomes a normal expansion of binary thought process.(Which we can call Objective) But the question is if the assumptions are false how can it get related to the Real World. The answer is beyond Binary. Simply understand that even if the base assumptions are partially true we should still have the Real link .. directly proportional the degree of truth involved in the creation. For example Pi which comes out of perfect circle doesnt find any respect in Nature. But at the same time near circle scenarios are common.There is nothing wrong with Nature .. it is the Maths which made some partially correct assumptions due to its subjective Nature. ================================================= Using Infinite Logical Bus as an example I tried to explain a simple fact that : Infinity doesnt make any sense as an iterative process in real world..(as a Noun you dont like nor do I) Maths doesnt recognize this .. I know but so was parallel law well established before it led to the discovery of a new branch within Maths.. Try putting in some logical questions to disprove me.

Just because we don't know about something doesn't mean it's not part of the universe, everything is part of the universe and when we find something new it changes the particular definition of the universe to include that new thing. REP: AS I said few things can not be found ever and yet it appears to palying a major role in the activities happeining within the Universe. Thus "everything" which by defintion gives a sense of knowledge reamins incomplete in its description. I have my own defintion of Universe. I give full credit to http://www.scienceagogo.com for making me arrive at this definition. Universe is Everything and it is Nothing.In other words Universe holds all the memory(past , present and future) and at the same time has no-memory of its own. I have given a theroy there called m-theory. It has been appreciated. Hope you guys will also like have look at it. ==================================================== And just to not a vacuum, is NOT void of particles, it is full of particles which are constantly being created and anihilated. REP: Yeah I agree. ================================================= I hate to disagree with everyone's definition here, but I have to disagree with everyone's definition The universe is a collection of processes, not things! REP: I do not disagree.But make sure you understand non-linear nature of any and all processes.Thus what you put in may or may not come out of it.An apparent violation of process law may take place. ==================================================== To say that it is merely an assortment of objects and things is confessing "Yeah, I believe in a Newtonian universe." General Relativity, on the other hand, argues that the universe is defined by what goes on within it. It is more like a tennis game rather than the tennis court. REP: Personally I also prefer to discuss Universe as manifestation of Ideas or Thoughts. ========================================================== What are they playing tennis with? REP: Who are they?

Instead of word unnatural .. it is always better to use the word disharmonious.Where is harmony stands for bringing in the soul of togetherness.

You've note defined 'number' still, yet keep talking about them as they have some well known definition that you're using. REP: Hope the reply gives you a more concrete answer to the actual status of Infinity. ============================================== A group is a group is a group. There are simpler algebraic objects, and more complicated ones. It is not 'incomplete' as a definition. REP: It is incomplete in the sense I explained above.. But still we have some more modifications to be made.

I only asked questions and didnt gave you any answer... But let me try .. What is meant by an Abstract Science? Is Maths really an Observer Independent Science? I am going to prove it otherwise. Why do we come out of Infinity and trust our understanding of it is right? Process of understanding infinity becomes easy if we construct a Logically Infinite Statement. for example : If there is any last representable Number N then additive property allows N + 1 . No where I am using time here to question its computability... Abstract world doesnt recognize Time as an Essential Element of Mathematical Thought. Therefore it is useless to argue using Time to the Mathematicians. Now I ask a different question: How many minimum number of Mathematicians are required to construct a real number set? Universe doesnt share this secret on the leaves of the tree and every child needs to learn these basics again. One has to deduce it from observation.Therefore observation is essential part of Mathematics... As the Maths is Boolean in Nature..and true and false reasoning is allowed to take place in Nature we need minimum of two Observers to explain the Mathematical World. In one observer world the deductions can turn out to be wrong. For example I may see only one and only one. Everything can appear to be a single Entity.Just like a Fish in the uniform pond with occasional occurence of waves..how this can happen in Actual Universe is a different question but is answerable using Physics. So I begin with relaizing myself as one but as I come across another observer.. he disagrees and claims to have a seperate identity. After much discussion we agree upon two. If two can happen then why not 3 or 4 or 5 and so on.(Multiplication is short hand for addition) depending upon the logically separate identity found in Universe. The disagreement continues and we end up with a very large number. But at some point during logical discussion we should understand something as vanishing from what was already understood as seperate entity. For example : A collection of Birds flying in Unison. or a group of Cells in Human Body or a close knit society. Therefore I suggest that after reaching a Sensible Number Limit we should reach to the One again in a logical Group.Instead of finding a flat spread of Numbers we should find a Circular one. Loosing all the information about numbers... except one. Let us call this operation N&1 = 1 Now the question is how can we loose information. We are so well connected. We have computers to assist. For an individual it means Death or a similar state. Which is inevitable. This is an observer centric answer.

Wikepedia .. wonderful attempt. ==== Here I come: The term universe has a variety of meanings based on the context in which it is described. In materialist philosophical terms, the universe is the summation of all particles that exist and the space in which all events occur which has an equivalent idea amongst some theoretical scientists known as the total universe. REP:Particles are the not the only thing existing in Universe. There is something called as Wave which is capable of Holding Information... without ever quoting the number the photons it used.It uses the Space.. without explaing its nature. I assume it holds the particles only. ======================================== In cosmological terms, the universe is thought to be a finite or infinite space-time continuum in which all matter and energy exist. (It has been hypothesized by some scientists that the universe may be part of a system of many other universes, known as the multiverse.) REP: Matter and Energy comes as a consequence of Universe and not vice versa.Universe has "Unknowbale" component as well. ============================================== The terms known universe, observable universe, or visible universe are often used to describe the part of the universe that can be seen or otherwise observed by humanity. Due to the fact that cosmic inflation removes vast parts of the total universe from our observable horizon, most cosmologists currently accept that it is impossible to observe the whole continuum and may use our universe, referring only to that knowable by human beings in particular. REP: Thats an excuse.. quite human I guess. ======================================

The real numbers are only a group under addition. No finite number of additions of real numbers yields infinity as an answer. It cannot or it would not be a group. You write the operation multiuplicatively. The reals are not a group under multiplication. The nonzero reals are. again no finite product of nonzero real numbers is infinity. REP: Thats exactly what I am trying to say. Ideally I believe that all numbers should hold same democratic right in the Abstract World. The exclusion should not have been so ruthless. I also believe that the current construct of a Group is incomplete. There must exist larger framework for handling it. ======================================================== Nothing holds us back from 'accepting' infinity, or more properly 'using symbols that are in some sense larger than any real number' for algebriac operations, they are just not elements of the set of Real numbers. REP: I am disappointed. Infinity no doubt can be understood as a Verb. But When I ask an Objective and Valid Question on the number of Elements in the Real Set ,what do I get in return...A verb(or the mathematical Sum). Consider the case of Parallel Lines. They are supposed to meet at Infinity in normal geometry.A set of parallel Line can thus very well represent infinity.Now if someone is asked to understand Infinity... then he will carry on the journey forever. He will never return from his logical bus to tell you whether he understood it or not.But we come back with intuitive reasoning that we understood it.And today we know that no such parallel line can be drawn in principle. The intuitive reasoning therefore has its own limitation. The situation of Infinity is itself hypothetical as there is nothing in the real world to relate to.(as of now) ==========================================================Just as we can extend the reals to allow i, and get the complex numbers. Incidentally the term 'real' in real numbers in no way is supposed to imply that these are 'real' in the ordinary language use of the word. Look up non-standard analysis or hyperreal numbers. Also try the extend real line. REP: I do not intend to relate real to the mathematical defintion of Real(Reality is much more complicated). "i" plays a role more fundamental in Physics.Therefore I wanted to know the real world significance. I looked up the Non-standard Analysis and found it very interesting.It only helps me to believe more strongly in the Number Democracy. ========================================================== "Infinity(whether good or bad) comes as a consequence of its existence" is in my opinion nothing to do with maths. I can't even decide what that means, if it means anything. REP: Its existence is denied by the defintion of Mathematical Constructs to avoid the grand collapse of its own defintion. ================================================== Infinity is not ambiguos and it occurs because we create situations that involve it. REP: A simple equation found in Nature E=k/t explodes to infinity at exactly t=0. t=0 is not denied mathematically but infinity is therefore t can not be exactly equal to 0.Thus t=0 also gets denied in the process.If we deny Infinity as measure then obviously in the above case we are also denying 0 as a measure of t. Here I have taken 0 but it can be any Number.(E-E1)=k/(t-t1) Similarly you have other equation's blowing up to the Verb at Speed of Light. ===================================================== Because physics is reliant on what is, not what seems convenient. REP: Convenience at the cost of Universal Formalization. ==========================================================

I'm confused with what this all has to do with the definition of "Universe." If it is defined as everything ever, known or unknown, then that's the definition. Where is the problem in that? REP: The problem is with defintion of Unknown...Unknown is not known till it is discovered.. Thus the existing defintion assumes Everything can be known about the Universe. Whereas I am saying that there are things which can not be known ever. Thus making the Universe in principle an undefinable identity extending beyond the realms of normal reasoning and observation. ======================================================= Why can the definition not include the "nothings", as you put them, of nature? REP: Good question... Hope you have understood Nothing. Now consider by usual logic a defintion of Universe: Universe is everything including Nothing... then stop as you say and understand the last word there is indeed nothing.I mean if you really understood Nothingness then you should hold no memory of any kind. You should have a Mind without any thought.... Thus what will be left will only Nothing.. and not everything. Therefore the defintion results in a collapse of Everything.. However if you continued reading till this point then you know that you havent understood Nothing. Nothing is a logical Blackhole. ======================================================= These things do not happen by chance. The waves are caused by wind, current, temperature, etc. Radioactive decay is caused by instability and the strong nuclear force (I believe). These are random but there is a reason they happen. I think your view may be a little strange. What do you mean by nothing? A vacuum? Or what. REP: The causes you mentioned are not the causes which can be related to Decay of a Radio Isotope in any way. Even if you get a detailed picture of Nuclear Force you will not be able to change its decay distribution .In other words it will not result in improved predictability. ==================================================== If a vacuum is not a vacuum by principle, what principle are you talking about? Vacuum is the name given to space occupied by no matter. REP: Vaccum is grand lab for Virtual Interaction.The net energy content at any instant is not zero. ================================================== If there is nothing, it is scientifically defined as a vacuum. Maybe you did not know the definition and "priniciple" of a vacuum. REP: Nothing logical and Vacumm is Physical.

Thanks for the cool reply. I do not doubt the precision with which Infinity has been left out... Let me take it from a Group Prespective,without getting into definition debate. I must admit that your defintion is very precise. But what all I am saying is even after the exclusion from the Real Domain why does the Infinity remains ambiguous and occures every now and then? Or why cant Physics get rid of it? Or why cant Maths be more Universal in its approach? Lets take Real Numbers as something belonging to a Group. Groups having various properties(additive , associative etc) But as all the laws are mathematical we will not dicsuss the real world.. Only those invented Mathematical elements which adhere to the properties of Real Number Group are included... Fine. Now this gives us an obvious reason to keep out the infinity from the Group. Interestingly the Group also claims to contain all the possible answers i.e. if you apply xyz operation defined by the Group on the Group members then you will get something within the Group.But the catch is you can end up with Infinity which we had outcasted ...!! So as a Mathematician what do we do? we define another Law in Abstract Space that such an such operation is not allowed or is not defined or requires special treatment.Which is not obvious and generic to the Nature of Groups.. Groups do not require it for their existence in Maths.. We ask for it. Therefore such a rule is an exception to the Universal Nature of Mathmatical Space.So the choice is clearly between a more Self consistent and holistic Theory and a Theory surrounded by restrictions within the defintion of Group. After all the processing done .. and all the relations found one has to come up with a set of possible Numeric Answers(Answer may or may not be True depending upon real Scenario.. the answer can be a simple constant which can be subjected to verification.. if its only exact final solution is something like "i" then I wonder why should I call it a solution in the first place.I dont know of any possible means to verify it. At best it remains consistent within Mathematical Space.... Now if "i" is acceptable then what holds us back in Accepting Infinity. Probably becuase the monster goes against the rules of its creator and forces us to outcast it. Once again I wish to state the same fact again that Infinity(whether good or bad) comes as a consequence of its existence in a Generic Real Number Domain. If and if there is no "real" challenge or equivalent to it then we must admit that Truth indeed oscialltes between Actual Reality and its Abstract tool(Maths is an Invention btw). ========================================================== the cardinality of the real numbers is 'a measure of quantity' and is not a real number. REP: Can you give me an example? ==========================================

A very smart question... Unnatural implies something outside nature. This is a useless word simply invented to serve different professions. Something unnatural in one branch of thought may not be unnatural in other.

Vaccum is not a Vaccum by Principle.Therefore it is not Nothing. Let me again explain Nothing - Assuming all to be an expression of Scientific Theory then it becomes obvious that Cause and effect are an intergral part of it.Can an effect manifest without a cause? Answer is Yes it can... Why a Radiactive Decay Takes Place? No reason other than the by chance. Similary why a Giant Wave (26 meters high) manifests in Ocean ... No reason other than chance. Chance gets influenced by the Number of Atom or Volume of Water. But the Principle Holds for Individual Atoms as well using Discreet Probability. So we say Decay of Atom happens purely by Chance. Its nature is to decay and "when" is guided by Chance. But "why" remains unasnwered as there is no known excat physical thing or event contained in the Universe which can be held responsible for it. Once we discover the cause we know the event is predictable and it is only a matter time when Experimental and theoretical Developements make it predictable. But when we say it is guided by chance in Principle we admit to the non-existence of Observable and knowable cause. Thus Nothing remains in Universe and it is realized in Principle. Everything includes Nothing. Now the question is if as an observer and a true Science Student can you execute a simple logical statement for sake of understanding Universe... Universe includes Nothing. You undertstand Everything and therefore Universe... next you try to understand Nothing. Nothing means you even forget the thought we carried you far... you forget that there is anything or everything. Thus knowing Nothing denies Everything. But since Nothing is part of Universe how can we allow it to deny the Universe itself(which most us believe as Everything). Please undertstand it carefully and you will see that Everything or every event is not sufficient to create the Universe. Accessing Nothing requires forgetting everything (including what I told you).

Traditionally Real Numbers are numbers which are rational or irrational. Or simply can be represented using non-terminating decimals. As I understand you believe Imaginary Numbers to be part of it...Am I correct? I had used only a subset of Numbers. And yes Infinity is an Element of Real Number... Set of a Real Number is a Universal Set.All the measurable qunatities can be expressed as using a Subset of it. In essence any Real question refers to Real Number System for Answers. Now my question was How many Numbers are there in the Universal Set...(If the question is real and understandable..which I think is) Obviously the answer must be found within the Set as it is a Universal Set of Real Numbers unless you give me a solid reason to Believe it otherwise. Thus the question is Self referral and Infinity must be an Element as well as part of it. I am not playing with symbols... I am translating a Computational Problem to a new origin. Thus seperating the Real Problem from a Mathematical Problem. Now the next question is : Is it not true that often the Application of Maths results in oscialltion of truth between Maths and the Applied Field.

Without insulting anyone let me state it this way R={-1,0,1,2,3 etc ....} No where I wrote Infinity. But Now the question is Infinity part of the real set of numbers or not...? Whether it is defined or not is different question. The answer is it has to be part of the Real Set otherwise the Numbers System can not be extended in Principle. We say that the Set can extended Infinitely... How many members are there in a Real Set of Number? (The question is self referral) As the theory dictate the answer has to be Infinite.. No one run away from the theory. But practically there is always a limit to what can be achieved.. Well practical is not part of Maths in many countries... therefore we will have to statisfy ourselves with Limit tending to Infinity. Now the question is Limit a Mathematical Tool or is it real? Consider another argument: In logical Deductions we are accustomed to tweaking of process to make it ok for physical applications.... When in reality this should not be the case. Assuming Binary reasoning applies to Real World. Then application of Science of Truths should not lead to oscillation between Maths and its application (Physics or Economics or Biology). At every step in the derivation we should be dealing with a Segregated Truths. By Boolean logic it becomes mandatory to maintain the integrity of Derivation. How is Infinity Defined...? Well this question is as good as asking what is maximum computing strength of Universe? How many points are available to represent a Number at any instant? In other words what is the Maximum Value Surface Area of Universe can represent? It is unkown but should be finite.Thus removing the need for Infinity. ============================================== I am personally very liberal with numbers including i. But what does it represent in Reality. Note that Ideally Truth should not osciallate between Maths and its application.Maths is an Abstract Science... consistent within itself. A good question .. I hope ==================================================== There is no consistent way to extend the fractional notation of a/b to accept 0/0, that is why it is genuinely meaningless in mathematics. REP: What I meant here was that you can translate the Number System to any origin and compute.... Thus a computational problem may not be able the actual problem... If I choose 0 as -1 then -1/-1 becomes indeterminate and not 0/0.. the respective understanding will also change. However it will help solve Computational Problem of 0/0 .Translation helps solve the problem of Computation but not actual problem which retains its relation to actual reality. =================================================

Everything includes Nothing.Isnt it? Or shall we choose to call Nothing as a concept outside Universe. Nothing is powerful concept.... it annihilates anything and everything.Much like Vaccum. Anyways if choose to call Everything as something what we have discovered and will discover then isnt it possible to discover Nothing. Nothing has no identification with anything known and has no capacity to be known. Understand Nothing as absence of any thought or any kind of Observation. If we choose to contain Nothing within some Boundary then we will still have something defined by its Boundary.

Universe: Everything. space, time, matter(anitimatter) energy, etc. etc. Universe: The collective name for everything that exists. REP: Everything is not known.Hence the defintion is incomplete. ============================================ Universe: All that is, was, and ever will be. REP: What was and what is and what will be are all unknown. Looking for a physical answer.

we have a distinction already between computable and non-computable numbers. REP:Yes this distinction exists for the convinience of Complete Computability. Maths doesnt deny the existence.All it says is such and such no. is non-computable to the extent of defintion of our Reference Point. ============================================== none of those is a real number (Ie in the set of Real numbers, which is the cauchy completion of the rationals), it is spurious to say something is a meaningless number when it isn't even a number in the first place. 0/0 is meaningless, fullstop (ie we do not assign it meaning, numerically or otherwise), infinity is ambiguous as a 'number', though handy. no idea what chess has to do with anything. REP: Infinity is ambiguous?? No it is part of Real Set of Numbers without which many Limits wont work and offcourse Induction Principle requires it to make the results Universally True(Making it true to the last attainable and any possible unattainable Number). As far chess is concerned let us replace it with an Computer being asked to perform Binary Search for based on 9x9 chessboard or 10X10 Chess Board and so on...notice that at some point of Time Computers shall take Very Large Time to Reach a conclusion.Thus making the Mathematical Problem redundant for practical use in immediate tournament. Humans can play in a much more complicated computing space which is a combination of Complex Congition skills and logic. Here we can say that a big Maths Problem (to the extent of Number of Branches it generates) gets replaced by Human Mind. Making the Problem appears Mathematical without taking away the pleasure of chess which still remains computable in Human Mind.Thus all numbers are not useful as they are limited by computational strengths to produce useful results. Consider another example : 2^32847928374987978987923 is my secret code which I intend to use in communication.Now I can compute it completely to know its property for encryption but I can also use it as series of digits and alpha numeric codes. e.g let 8 stand for *.. the meaning changes it no more remains a number.It becomes a comprehensible code. Thats why chose the Chess as an example to define a Large Number with precisely defined purpose. 0/0 is meaningless to the extent of Convinience.... All it means is that there no property of such a state which can used to improve understanding. Square root of -1 is non-sensical but works because it has well defined properties. Loosely this applies to Infinities as well . But it remains a problem as well in the form of singularity in Physics. Anyways the question was on Infinity. We say is Infinity can not be reached as it is at the Horizon of Mathematical Thought. Can we say the same for 0 ? Let us look very closely at 0 and its meaning. 0 doesnt represent Nothing. It is always represented as a finite State in Computational Domain. It can be -ive potential or some relatively lower finite potential.0 Apples doesnt mean Nothing.It means there are no Apples. What if I choose to call 0 as 1? I mean isnt it possible? Let Absence of an Apple be called 1 then we have 2 , 3 apples defined accordingly. Cant we perform all the Mathematical operations without falling into the trap of Infinity and Indeterminate State?All we will have to change the corresponding Understanding as well.. and thats all. This shows that Problem is purely Mathematical and it does not mean or should not mean incomprehensibility of Mathematical Situation.But here we have shifted the Problem some where else. Thus to attain complete comprehensibilty using Maths Infinite Number of Transformations will be required.Which by defintion of Infinity is not Possibile. Therefore Universe can not be understood entirely using Maths. =========================================== strictly speaking i is not in R, but in an extension of R, so you need to explain what you consider a number to be exactly before you start dismissing things as meaningless examples of them. REP: The reason I gave are straight forward. ================================================== Incidentally, all known discrete models of space are 'inaccurate': they make physical predictions that are observably false, so it is a little premature to say everything happens in a quantized way. REP: Inaccurate in a fundamental way. It says there is a limit to accuracy which can achieved....Physics shows it using Uncertainity Principle. The reasons for this inaccuracy I think is embedded in our approach towards the understanding of Universe which is entirely Boolean. ===========================================

Good question. Infinite set of Numbers and Infinite set decimals are two basic assumptions of Maths. All such computational truths are limited by the computational strengths. Consider my definition of a meaningless number: A meaningless number is number which is known but can not be used for any computational purpose thus making the knowledge useless. For example 0/0 , Infinity or some arbitarly complicated Chess Game in which the rules change as the game proceeds. Unlike imaginary number "i" which has found its physical use. In principle there is a limit to finding a meaningful number from an infinite set. Today which is largest number which can be represented and used? Ofcourse we will find some answer. It is not unanswerable. Tomorrow this limit may get extended but it still remains finite. Thus the possibilities are infinite but realization is finite. When an ant covers a distance between two ends it doesnt take infinite steps. In reality things happen Quantized way.

Morality is a system of value judgements that attempts to define natural human behavior and distinguish this data set from unnatural human behavior. Humans are capable of both kinds of behavior. Without morality, the unnatural and natural become relative, with unnatural having the advantage, requiring less reason and will, and the ease of unconscious compulsion. REP: I do not think so. Morality is the social obligation invented to achieve higher level of togetherness. They are hard coded in to nature but are invented to keep the chances of survival maximum. Most of them are based on instinct.

The deal between nature and observer is very strange. What it presents as coincidence can be shown to be major life turning moment in one's life. Aparently making Success look as a series of coincidences. It happens in case of finding mate or job or starting a new business. Definition of Conincidence depends on your understanding of Complete or limited comprehensibility of Universe.

Homosexuality is not unnatural. It has been proved using psychological questionaire. Many species appreciate it. However the number of such high end sexual behaviour is limited. Majority doesnt believe in it. Today reproduction is not an issue but still there are good reasons to believe that Homosexuality can not be adopted by majority. First Nature itself shows very limited evidence. Secondly by nature every human relationship suffers from its shortcomings.Once the concept looses oppostion it will die its natural death just like heterosexuality. However it does not mean that those who practice it are not Godly.

Hi , I am new to this forum and wanted to know the defintion of Universe... What is Universe ? I have been discussing at http://www.scienceagogo.com but it appears that no one has far been able to give me the answer. Regards, Dheeraj