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 May 6th, 2013, 04:09 PM #1 Banned Camp   Joined: Aug 2012 Posts: 153 Thanks: 3 Relative Mathematics Relative Mathematics By Conway Noel Lovett Chapter 1 All numbers can be represented as two independently existing, interwoven functioning things. As the title has implied, I say now blatantly. The ideas herein are heavily weighted by that of Albert Einstein, and his philosophical principals of relativity. I in fact, am saying that �as space and time� are two independently existing, interwoven functioning things, so also are numbers. That is relative mathematics. I maintain that relative math will be a highly more efficient, accurate, and attainable to understanding, then the current form of mathematics. Several of the current axioms of basic arithmetic will be able to be reduced, and or completely done away with. I will show how these four simple axioms are no longer necessary. 1. Commutative property of multiplication 2. Multiplicative property of zero 3. Multiplicative Identity Property of 1 4. Inverse property of Multiplication. Infinity its self will become better understood. And even the mysteries of pi, can be de-mystified. In short, relativity is a necessary philosophy that has yet to be applied to mathematics, and mathematics is in desperate need of it. I will say, once again the reality, that space and time, are relative. So then should not the �tools� by which we measure space and time also exist as relative, these tools of course being mathematics? One may already be asking, �If you say that all of math is wrong, how then have we gotten it right so far?� By having it �right� I suggest that our level of technology is applicable as a defendant for the current system of mathematics being correct. The idea for me is that, it is NOT that I am saying the current system is wrong. It IS that I am saying the current system is incomplete. That what the system needs is the applying of the �principle� of relativity to it. The �general philosophical principle of relativity�, is that space and time are two independently existing, interwoven functioning things. In short space and time are two things in one. This may be considered a crude simplification, of the great works of Albert Einstein; however I feel the simplification of its truth necessary for the application of it to mathematics. So I say then that any given number, can be represented as two independently existing, interwoven functioning things. Much of this is all ready �inherently� done by mankind. But if it is not �directly� done, then one may always say that full awareness of the system has not been obtained. As a result, some of what I say will sound to the reader as �inherent� explanations. I am certain however that such tedious explanation is necessary for the application of relativity to the current system of mathematics. Chapter 2 All numbers can be used to represent things, or ideas. All ideas and things contain value and space. Any given number, whether applied to an idea or just used abstractly, also has a value, and a space. So that if I have the number 2, it is that I have 2 of 1 thing, what ever that thing might be. This is what I mean by value. It is also true, that 2 can be represented as space. I do so as, ( x, x ), or the space of 2. So then in regards to my previous statement, I have 2 spaces, both occupied with 1 thing. When I use the symbol for the number 2, the quantities of space and the value, are inherently understood by the observer. That is to say one does not have to ask does the number 2 have space. If I say, or write 2, my previous question does not need to be asked. However to continue I must be able to come to a general consensus as to the specific labeling of the parts involved in the meaning of the number 2. I will hope we shall agree that henceforth, the symbol for the space of any given number is a group of the generic variable X, whose sum is that of the given number. That is that the space of 2, is written as ( x,x ). The space of 3 is written as ( x,x,x ). And so on. The value of a number shall retain the same symbol as its number with the added variable of V for value. That is the value of 2 is 2v. The value of 3 is 3v. And so on. Of course the symbol for any given number shall retain its current symbol. I shall continue by offering definitions. Value � Labeling of quantities of existence. Space � Labeling of quantities of dimensions. Number � A given combination in the given amounts of Value and Space. As I mentioned earlier, we already �inherently� distinguish the differences of these two things. This is understood in the following. There are technically four versions of the symbol 2. All four symbols indicate a different value, and space, unique and separate from what is represented by the number 2. That is we have ( .2, 2, .02, 20 ), or four versions of the same thing, all with different space, and value. And from this we can see that the potential for an infinite amount of the symbol 2, that can be derived. If we were to ask ourselves what is this ( . ) and how does it�s placement with 0, change the value and space of the symbol. We can only answer by explaining that the �decimal� is a �mark� or counting of space. That is on a number line, .2 has less space to 0, then 2 does. Therefore .2 is less than 2 in value, and in space. The decimal is an �inherent� labeling of dimensions, or space. And it is the dimensions of space that inform us of our defined value. This is also true of fractions. When one sees a number written in fraction form one is inherently informed that the numbers space and value are relative to another number. There are also interesting effects with fractions and relativity that I wish to discuss latter. Also I wish to address the �inverse property of multiplication�. I say clearly that value can NOT be infinite. This is a quality that can only be applied to space. This is best understood with the number .9infinite. I can say that a singe .9 is smaller than .99. So then unless I can write, or possess and infinite amount of .9v�s then my number is NOT infinite in value, but only in space. Consequently If I did have an infinite amount of .9v�s then my number would become the number 1, which is then a finite value, and space. I can then say that .9infinite is equal to 1. The consequences of relativity and infinity are significant. I wish however to address these ideas in a latter chapter, as well as it being necessary for the reconstruction of zero, and the number line, themselves before addressing infinity. So I say clearly that, value can not be infinite, space can, or can not be infinite. A number on the other hand, can be infinite, but truly, it is the space that composites the number, that is infinite. So then while a number can be infinite, it is only its space that is holding this quality. I wish to address this further latter. Hopefully I have clearly defined what the two separate parts of any given number are. Value and space, and with these two things, we then have the bases of relative mathematics, and with which I may continue. Chapter 3 The idea of relative mathematics is not applicable to the idea of addition. That is to say that with addition we have both the value and the space of the given numbers inherently declared in the equation. With the equation ( 2 + 2 ) we are observing both symbols as the number 2. So then both value and space are accounted for. This is so for any version of the symbol 2, or any version of any value. But this is not the case with multiplication and division. It is the case with multiplication say ( 2 x 3 ) that what we have in this simple equation is not the symbol number 2, and the symbol number 3. In fact the number 3 does not exist at all. Proof is in the understanding that what we have �collectively� decided as humans to be the explanation of this equation is that what we have actually is ( 2 + 2 + 2 ). So then what we have is, three symbols of the value 2v, and then added. This of course is reversible. We can also say that what we have with the equation, ( 2 x 3 ) is then ( 3 + 3 ). Or two symbols of the value 3v, then added. This can be viewed as the fundamental axiom of the �Commutative Property of Multiplication�. I will show later that this property is not even needed, and can be entirely done away with. This will also be the case with the �Multiplicative Identity Property of One�. So then to apply the relativity, what we are saying with multiplication ( 2 x 3 ) is that, what we have is the symbolic value 2v and ( x,x,x ), or the space of three. As stated it is possible to say that what we have is the space of 2, or ( x,x ), and the value of 3v. So that in multiplication we are NOT looking at the real symbolic number of two, separate numbers. But rather we are looking at the symbols for a single value, and of a single space. So then in multiplication one symbol is for value. The other written symbol is the symbol for space. As long as the previous outlined definitions, for that of value, and of space are adhered to, then can we continue without the need of declaring a �Commutative Property for Multiplication�. This also, so long as one clearly defines the operating rules for the interchange of a value and a space. I will now do so. The first rule of multiplication is this. �The value is always first, and the space always second�. Now in reality it matters not which comes first in the equation. It only matters that we universally concede as to our unit of �measurement�. Or simply that we always perform the equation in the same order. The �order of operations�, can be an example as to this. It matters not which operation is truly first in the calculation of any long equation, so long as we always perform it the same. The second rule of multiplications is this. �The given value is applied to all spaces, in the given space, and then added. The sum is the answer.� With these two rules no further explanation of multiplication is necessary, nor is the �Commutative Property of Multiplication�, or the �Multiplicative Identity Property of 1�. This can be seen with the following equations. If then we have ( 4 x 3 = 12 ). Four as the value, 3 as the space, ( 4 + 4 + 4 = 12 ). ( 3 x 4 = 12 ) Three as the value, 4 as the space, ( 3 + 3 + 3 + 3 = 12 ). It then is the value that is changing, in the reversal of the equation, and also the space. One may now be asking about zero and multiplication. But again there are things I must address before continuing on that path. I can say however. That what I have set forth as the �rules of multiplication in regards to relativity�, will be strictly adhered to by be. Also no further rules regarding multiplications functioning will be added. In short with a redefining of zero, one can drastically reduce the amount of axioms it requires in regards to operations. I shall now address subtraction and division. They are by nature inverse of addition and multiplication. This has not changed with the application of relativity. As a consequence it will require much less effort to define. Assuming one has followed the principles of addition. Subtraction like addition does not have an application for relativity. That is to say that with it also we are observing or writing the symbolic number in all cases. That is in the equation ( 2 � 1 ), it is the number 2 and the number 1, that are being subtracted. But this also, and again, is not the case with division. Division like multiplication is an equation that contains a single value, and a space. So that if we have ( 6 / 3 ). Six is a value, and 3 is a space, or ( x,x,x ). Also the same with its reversal ( 3 / 6 ), 3 is the value, 6 is the space. What changes are the rules for application, and they are as follows. The first rule is �The value is first, the space is second�. The second rule is �Subtract evenly the value given into all spaces, in the given space, and then subtract all but one value as your answer.� I will leave it to those that desire, to see this in operation. In short division is the inverse rules of multiplication. This of course is because subtraction is the inverse of addition. I hope to have explained the application of space, and value to multiplication and division. Again zero with be addressed herein. Chapter 4 At this point I must make a switch in topic in order to later better explain my self. In this chapter I will be addressing the reconstruction of the number line, from a philosophical viewpoint. This will then be used, after the reconstruction of zero, to explain multiplication and division by zero. Some readers may find it odd that I referred to the philosophy of a number line. This is because no one has really defined what a number line actually is. It is inherently understood by all. All that must be done is for one person to draw a line, and then put numbers on it. Even in any order he chooses. As long as the observer is fairly astute, then they themselves now �understand� what a number line is. In short it is a line, with numbers assigned. I think however that this definition is woefully inadequate for our purposes with it, and for the explanation of it. I shall define is clearly. A line is space, with values assigned. And what is better than the word space, to define what a line is. Surly we can use the old explanation for a line and say it is many, many dots all connected. But this is not true. The line �theoretically� never breaks. To draw a dot next to another dot you MUST show a break. Otherwise you only make a single dot bigger, and then if continually done, turn it into a line. And a line is clearly not a dot. And what is a break, if not space. So then if a line is a measurement of space, and the numbers assigned are not numbers at all but instead values. Then once again we can see how relativity is applied to mathematics. To continue, if we were to draw a regular number line, how then to we declare the assigning of the �numbers�. I have already mentioned that technically they don�t even have to be sequentially placed. But what does matter is that we use a DOT to show where one �number� is, and another Dot, to show where the other number is. It is in this case we say that the DOT is the number and the line from dot to dot is then space, or any given value found sequentially between the values on the dots. But if in the latter case we say that they are values, then does not one have to have space between the �dotted� values in order to place more values between them. In fact no human, can draw a number line with out the use of space. A number line is clearly composed of space, and value, whether any given �spot� on the number line is value, or space, is relative to the dealer. That is to say on a number line any given spot on the line can be a space or a value depending, on what the �person� drawing that number line has intended for the purpose of it. The line that is, is then a number by definition. In that it holds both a value and a space, and it is representing them at one time. So then a �line�, even without numbers on it, is another symbol for a number. But its value is undefined. Its space is clearly defined by the length of the line. This is to say that any given number can then represented by it�s parts, (value, or space) being either defined or undefined. This I shall get into depth with later. At this point I shall say clearly that we must construct the idea of a �reference point� in order to continue with the construction of the number line. The �reference point� is what is needed to apply �operations� of mathematics, or addition and multiplication. I must then define what I mean by �reference point� in order to show how �operations� function with a number line. I can begin to define a �reference point� by drawing two separate number lines that are in whole truthful, yet entirely opposite. ?----------1--------2---------3----------?, and 1 2 3 ?--------(---------------)(---------------)(---------------)--------? What has happened here is a change in point of reference, or relativity. The reference point being the position of the �number�, or value assigned on the number line. When the values are placed on the number line then the values become numbers and the lines between become space, or sequential values. When the values are placed above the line, the brackets become space, or sequential values composing the overhead value and the numbers are components of all that is between the brackets. In short with the latter line the brackets as a pair, seen wholly, is a number. The line observed individually, between a pair of brackets, is space. This should represent quite well, the interchange of value, and space. This should show clearly that space, and value, while being to separate things, are interchangeable in their interactions, and relationships. This event of interactions is what we call a number. And clearly defined it is our point of reference that is the major catalyst for our change of our reference point. In short it is when one changes their reference point that relativity has come into play. And changing of reference point, and values, and space, are the key components for relative mathematics. To continue I will give a finite definition that can be adhered back to for the idea of �reference point�. A reference point is �an applied number on a number line whose value is undefined, but space is defined.� To be clearer I must say that undefined value, does NOT mean the absence of value, it means the value is NOT known, but value IS there. This is as per the rule I applied to a number line. It is by definition a number, even if no numbers are drawn on it. In all case on the line there is both value and space. It is that in some cases value is known or not known, and space is known or not known. This I consider to be a partial reconstruction of the number line. I think it helpful to at this point to reconstruct zero in its definition. After this I shall then reunify zero and the number line to complete the definition and use of a number line. Chapter 5 I pick up right where I left off. If then by definition a �reference point� is a number whose value is undefined, but space is defined. Then zero functions according to this definition. There are many different ways to use a �reference point�. To say that my reference of the lake was from the docks, as opposed to my reference of the lake was from the campsite, is an abstract example of the use of a �reference point�. This was the kind of �reference point� I was using earlier with the visual construction of my number lines. However zero can be defined and applied specifically in a purely mathematical way, relative to a �reference point�. That is to say that zero as a number has a undefined value, and a defined amount of space. Zero is then a reference point. As to which all numbers are then referred back to, there by allowing them to have a defined value. So clearly one must have a reference point to have a defined value, otherwise there is only undefined value. If I stated earlier, that the entirety of a line, defined or not, posses value, and if I then want to start �marking� the value, I essentially have to take a guess and say, at �this� given point I do not know what the value is (because nothing on the line has been labeled). So I then make it my reference point and from here using an equal amount of space begin marking values, thereby creating numbers. Additionally, at this same given point I will use the symbol 0. It has an undefined value (because of no previous assigned value on the number line), and it has space. Zero undoubtedly occupies space on the number line. Abstractly I can say that I can not even write, or imagine, a �thing� on the number line with out space, because the number line itself is space and value. I have to �use� space, from the number line, in order to write zero. But this is just abstract. If I use the number line, I can apply an equation that proves zero occupies space. It is a true statement when I say, all equations, can be represented on a number line. That is to say that if I have ( 1 + 1 ). I start on the number 1 and move 1 space to the left, which gives me a value of 2. But if I have the equation ( 1 + (-1) = 0 ), then the only way to state this equation is to say, start on the number of 1, and move one �space� to the left, which gives me a value of 0. I by definition of the equation landed on a spatial value of undefined, or my �reference point�. But If my reference point did not contain space, then the answer to this equation would be (-1), or the next value and space to the left of 1, on our number line. Also I should say that value inherently requires space to exist. Can one not ask another to give any value of any given thing, and do so with out the use of space? Abstractly this can not even be done. If I were to ask one only to think of an idea, or value, one can not do so with out space. This is to say than any given man can only remember a given amount of values, at one time, to remember more requires better memory, or more �space�. I say in fact that if they are only thinking of one thing, then that thing they are �thinking� of is its self occupying space. But because it is undefined in value, that is I can not show you the value of what I am thinking, does not mean it is devoid of space. Can one not say that it is the brain that is thinking; therefore the space the brain occupies is substitute for the space required for the thought to emerge. This can be said another way, is it not the neurons that are firing that make the thought? Therefore it is the space of the neurons, in a state of firing that gives rise to the space of the thought, again whose value is undefined. It is at this point that I may now lay down new fundamental definitions of the number line, and zero. After which we may then reunify these two things in order to then discuss their process in relation to operations. Zero � Zero is a given defined space, on a number line that is undefined in value. (But value is still present). Number Line � A defined space with an undefined value. May 6th, 2013, 04:10 PM #2 Banned Camp   Joined: Aug 2012 Posts: 153 Thanks: 3 Re: Relative Mathematics part 2 Chapter Six So in the simplest of terms, if we wish to �place� zero, on the number line, using the aforementioned definitions, we must then say that zero is a defined space, within a defined space, which has a value undefined, amongst a greater value that is undefined. So this would be then my definition if I were to apply zero to a number, and this definition holds true no matter which of my pre-used number lines I chose to use. ?------------0-----------? or, 0 ?----(--------------)----? In the first number line the symbol 0 occupies space, that of which is required to draw it, and its value is undefined inherently with the use of this symbol. In the second number line the space of zero is what is drawn with the brackets, not the symbol, and the value is placed over head to show that it is the entirety of the given space that constitutes the value of zero. Again the value of zero is undefined, strictly because no values were previously assigned to the number line. Also again, the number line, its self, in both lines, is an amount of defined space (noted with the arrows), and an undefined value (because no values have been assigned, other than a reference point, or zero). It can be simply stated then that a number line by its self is undefined value with defined space, and then that a number line with a zero is defined space, with another defined space within it, and no defined values assigned. It of course then follows that once we have 2 defined spaces, one within the other, we can then begin to define values. Or make numbers other than zero. So zero functions philosophically as a reference point, and mathematical as a reference point. Once it has been constructed, in any given of the two ways, we then can begin to assign defined values. ?----------(-1)------0------1----------? or, -1 0 1 ?--------(------------)(-------------)(------------)--------? This of course has a very interesting affect on the understanding of positive and negative numbers. Infinite also will come into play here as well. I wish again to hold off on explanations of infinite for a moment, and address positive and negative numbers. I will restate the definitions of positive and negative here. Positive - A given direction of increased value and space from zero. Negative - A given direction of increased value and space from zero. This follows from, a line having 2 directions, or dimensions in its nature. I will clarify that if we have 1 dimension we have 2 directions. That is a 3 dimensional world has 6 directions. If then a line is drawn and it has two directions. As I mentioned earlier, these directions are space, of which we then mark, If then there are two directions to a line then there are two ways in which to increase and decrease the makings of it�s space, and it�s value. And positive and negative are merely the indications as to which direction one moves in there increasing and decreasing of space and value. This is then to say that -1 is not really opposite of 1. It is that it is a single space, and value, in the opposite direction from the reference point, equivalent to that of 1. But what we MUST note here is that the values of 1 and -1 are in reference to the value of zero, which is undefined in value. So we may say nothing more of -1 then that it is equivalent to 1 in value and equivalent in space. This is because the value of -1 and 1 are referred back to a number whose value is undefined. There real value is not known. But for the purpose of use we declare there value by using a �reference point�. We may then consider them opposites, but only with the understanding that they are opposites in reference to zero, but not opposites in reference to the �number line�. This can be better understood by saying, if we have the number line. ?-----7-----8-----9-------? But I only give you question marks or, ?-----?------?------?-----? and then ask you to find a way to use this number line, then you could only do so by putting a zero on the middle question mark and of course a -1 to the left to show direction, and a 1 to the right to show direction. But the value of the middle question mark, had been defined, I just did not define it to you. So you were then forced to use a reference point in order to make use of the line. This also brings up the idea that the marking of space is equivalent in size for all numbers. This does not have to be the case, but it is so for easy understanding and use. This is to say then that the space of 1, on a number line, is equivalent to the space of 2. But the number 2 has the value and space of both numbers, again to say that 2 is 1 twice. And 1 and 1, or 1 twice, is equal in space and value. I may also say now as a clear axiom of relative mathematics, that the space of 1 is marked equivalently to that of its reference point or 0. So then the space of 0 is to be marked equivalently to the space of 1. ( x ) is the symbol for both the space of one and the space of zero. It is said, �You say potato, and I say pototo.� This is an example. It matters not the length of space used to mark the space of 1. So long as the person doing so always continues with the same amount for all numbers, including zero. With this done, I can now return to multiplication, and division by zero. Chapter 7 It is at this point that I intended to show that our current interpretations of zero and the number, and their relationship with operations, are currently incorrect in mathematics. I will say now clearly that ( A x 0 = A ), and ( 0 x A = 0 ). These equations are based on the previous definitions I gave for multiplication, and zero, and the number line. I can show this visually, and step by step for ( A x 0 ). If A is my value, and 0, is my space, then I have ( x ), the space of zero, and I replace all spaces with the value given. So then I have (A). The last of the rules for multiplication then say to take the sum of all spaces. This is then A. Not 0. This follows through for the inverse of this equation. If I then have ( 0 x A ). I would have the space of ( A ), then replace all the spaces associated with A, with a zero, then add all the zero�s and arrive at the sum of 0. I think more importantly then the actually performing of the operations, is the simple physical argument that follows. If I have A, in my hand, and I add an A, I have 2A. If I then have an A and I multiply it by 0, then how is it that the A has disappeared, according to the �Multiplicative Property of Zero�. There is still an A in my hand. While one may say that we can not say multiply the A by 0, because A is empirical and multiplication and 0 are not. But we can add A�s to zero, and visa versa, and so empirically. So then why, can we not multiply A�s abstractly that exist empirically in our hands? This then offers that the given property of �Multiplicative Property of Zero� is inherently wrong. Not only with use of linguistics but also in use of the abstract symbol�s for space, and value. It follows also that it is wrong if we perform these operations containing zero on the number line. I will at first return to addition. ( 1 + 0 = 1 ) represented on a number line is, and following the rules for �Identity Property of Addition�. ?--------0-----------1-----------2--------? The operation says to start on the 1 and add all the values, and space of 0. If then as declared before the space of zero is defined as equivalent to that of 1, and its value is undefined, then we are adding a defined value of 1, and an undefined value, with two equivalent spaces. If then part of the defined value is also undefined, what is done? Is it not understood, and agreed that adding zero changes nothing. So then if I start on the number one and �add� the number 0, I have not moved, or progressed in either direction of the number line. This leads us to a fundamental axiom that is already in existence. It is the �Identity Property of Addition�. Is it not also true that a collection of value, that is partial defined, and partial undefined, is of no use, and must be defined; therefore the undefined is �dropped� do to its inherent nature of being unknown? I shall endeavor to be less ambiguous. If I add a value to a reference point all I truly can say that I have is the value, and the reference point. But if the value of the reference point is undefined then it is useless to addition. No symbol can be written to add an undefined idea/value to a defined idea/value. But one does know beyond certainty that the value of the other symbol existed. So a partial value is known, and being that the other value is not, it is not mentioned or declared, again leading us to the �Identity Property of Zero�. This lengthy explanation is not necessary for multiplication. As I have stated that when adding both symbol�s represented are that of a number. But again in multiplication and division this is not the case. The value is first in the equation, and the space is second. If then the equation is ( 2 x 3 ). And I wish to represent it on a number line; I must then first declare how multiplication is performed on a number line. If then I have a 2v, I start off on the number 2, and I add all values that are contained in the equivalent space of 3, so then on the number line. ?-------0(---------1-------2)(--------3-------4)(------5------6)------? The first set of brackets is the space and value of two. It is then added 3 times. The other sets of brackets being the two sets of space, and value that are equal to the first set to compose the three sets, or the space of three. The sum of all independent values and space is 6. This again is important to note that the first set of brackets has two values, inherent in it. The value of two number 1�s, or the space of two with the value of 1v filling them. So it can then be said that there is 6 independent values, and spaces in this number line. There is one mark of value for each independent marking of space. Only when we want a number do we then combine these independent values, to compose a greater value associated with the number. So then with the equation ( 2 x 0 ). The number line is, ?-------0(-------1-------2)-------? If it is then that we have the space, and value of 2, and we add all spaces, and values of it�s reference point or that of zero, we then have the defined space of zero, the undefined value of zero, and the defined value, and space of 2. The sum of course is that of 2, again in regards to the �Identity Property of Addition.� I will say then that ( A / 0 = A ), and that ( 0 / A = 0 ). These equations are again following the assigned rules of spaces and values, and there relationship with operations, and the number line. I will entrust that it is not necessary to perform these operations on the number line, or with symbols of values, and groups. All that is necessary to arrive at these conclusions is remembering the original rules set out, and that division is the inverse of multiplication. Chapter 8 I shall now address the concept of fractions. I think it important to point out that in all cases of multiplication it is in fact indirect addition. So that then if we are dealing with fractions and their multiplication, we are also dealing with indirect addition of fractions. But it is relative to a very specific idea. This idea is already inherent when one observes the symbol of a fraction, or decimal. The idea being that what is being observed is a piece of a whole. That is to say that with the number .25, or the number �, we are observing a piece of the value, and space, of the number 1. Essentially the application of symbols for numbers and space can be easily applied to fractions, and decimals, but it is again under the understanding that what is being observed is relative, and it is relative to what symbol is the space and what symbol is the value. To set forth definitions, I will say the following. In regards to the multiplications of decimals, this is not possible. The reason being is that a decimal is only a representation of another number specifically for the purpose of simplicity. This is to say that .25, is really the number �, or the fraction. So then if we substitute any decimal for its equivalent fraction, we can then continue with our operation of multiplication. It is continued, with the following definition. When the fraction is used as a space, the numerator and denominator are assigned the generic variable x, in accordance with the sum of the value for each. This is to say � as a space is ( x / x,x,x,x ). And that the space of 4/3, is ( x,x,x,x / x,x,x ), and so on. With this understanding all one needs to do is continue on the original path defined by that of multiplication. This is to say that ( 1 x ( 1 / 4 ) = � ). So that If I have the space of ( x / x,x,x,x. ), I then replace all spaces with the value given or 1, which makes ( 1 / 1+1+1+1 ), then added, or ( � ). Or I can show it with a value fraction, into a space fraction. I must add herein a new axiom. �A value fraction is put into a space by replacing only the numerator�s value, with the numerator�s space, and that the denominators� value is replaced with the denominator�s space. This is also true of adding a whole value into a fractioned space. It is not necessary, as we can see with the above equation. If we have a value of 1, it can be rewritten as 1/1, and thereby applied in the same fashion as a fractioned value. If then the equation is ( � x �.) I have the space of ( x / x,x,x,x ) I then replace all the numerators spaces with the numerators value, and then the same for the denominators value, with the denominators space, and arrive at. ( 1 / 4+4+4+4). Or ( 1 / 16 ). It is here that we can see that the �Inverse Property of Multiplication� is also no longer necessary. If one were to apply the symbols of value, and space one can see �inherently� why this is no longer a necessary axiom. Also this kind of operation raises a very interesting question. Why is it then that when two whole numbers are multiplied the answer arrived at is larger than any of the numbers used in the equation, but when two fractions are multiplied the answer arrived at is smaller than either two numbers used in the equations. This is of course barring any use of zero, or a reference point. This unique result is also applicable to division. That is to say. If I divided two whole numbers the answer arrived at is less in value than either two numbers used, and if I divide fractions the answer arrived at is larger than any of the two numbers used. Mathematicians have of yet to explain why this is. In fact if an astute student where to ask this question, they would not even receive an axiom, such as that of the identity property of addition. I may ask why is it, that anything plus 0 is itself, and visa versa. But the answer is with that of an axiom, that is to say it just is. Even though I feel I have offered an adequate reason for this axiom. It is however curious to note that no such axiom exist for the inverse property of multiplication of fractions, and whole numbers. Here in I shall try to explain this to the reader. It is inherent when one observes a fraction that again one symbol is a value and one symbol is a space. That is to say that as a stand alone symbol any given fraction is two separate symbols, relaying two bits of information. I will now declare them directly. If then the fraction is (1/4). It is that we are observing the value associated with four spatial divisions of the number 1. This is that if we divide the space of 1 into four spaces, and the value inherent in 1 space of this collection of four is now our total value. So then in a fraction the numerator is the value, relative to the value of the whole number, divided by the spatial value of the whole number, grouped in a given fashion. Or the numerator is the value, and the denominator is the space, and they are relative to the whole number 1. The reason for this is to show that when we add fractions we are manipulating values, and groups inherent in the number 1. This is to say that if we have ( � + � ), what we are doing is adding two fractional values of 1, with two fractional spaces of 1. So then when the two numerators are added as fractional values we receive a new value, whether or not it is a fractional value is relative to what happens with the adding of the fractional spaces. If the sum of the fractional spaces becomes equivalent, to the whole, or 1, then the value is no longer fractional. If the space is less than or greater than the whole of the spatial value, then the value is fractional relative to the new space that is created, by the rules of addition with fractions, or the process of finding common denominators, or common spatial marks. It is with these rules and understanding of fractions that we can understand that it is not that the product of multiplied fractions that is the inverse of multiplied whole numbers; it is that the manipulation of values, and space, is different for pieces, then for wholes, thereby creating this illusion of inverses. Chapter 9 I would now like to discuss relativity and infinity. As I have already mentioned it is that relativity shows us that infinity is a concept that can not be applied to values. It can only be applied to spaces that, with any given number that is infinite it is not the value that is so, but it is the space that is infinite. So then 9-infinte is not an infinite value of 9v but it is a value of nine 1�s, then with an infinitely defined space. This is best represented in use of the number line. To do so with simplicity I will use small numbers, but the application is equivalent with indefinitely large sums. So then if I have the number 2 infinite, it is represented on the number line as this. ?----x----0----1------1----x----x----x----?. I have abstractly shown with this number line that the x�s, are infinite, therefore, infinite space, or undefined space, but the value is clearly defined as 2. This is separate from the regular number of 2. It as a number line is as this. ?----0-----1-------1----?. Only two spaces are defined in value and in space, aside from the reference point, and therefore the number 2, but not the number 2 infinite. This is also how we understand the equivalency of the number .9-infinite and the number 1. Likewise the number .2-infinite and .3 are equivalent. This can be summarized as an axiom that states the following. A value that is infinite is equal to the next sequential finite value, on that number line. This of course raises many more questions. Such as how infinite works in groups, such as those suggested by George Cantor. This also will have an effect on how the number pi is viewed. If then a value can NOT be infinite, but space can, then when we consider the number pi, what we have is very unique. If then we observe the number 3.14infinte, we are observing defined value of 3.14, with an infinite space. This of course changes with any value, chosen for pi. The only other thing to note of pi is that it is true of physics to say that a circles circumference is a little more than 3 times its diameter. If one wishes to obtain more and more clarity then what is necessary is an increase in value of the number pi. This should serve I think as a clarification of pi, reducing some of its mystery. If then the number pi at any chosen version, has a defined value, but an undefined space, we can understand in a much simpler fashion how pi is not truly unique, other than it�s relationship with geometry, and circles. As of yet I have to fully explain the concept of infinite and relativity. I shall continue with the implementation of the number line and zero. I begin by saying that an infinite number is equivalent to that of zero, in that it has an undefined value. But what is different is that the value is undefined as greater than or less than zero relative to it�s location on the number line, from that of zero. What is different is that zero has a defined space, but infinite has a space that is undefined. And it is undefined as less than or greater than zero, in relation to its location from zero. I can show this on the number line. It is also worth noting that infinite is very close in operation to that of a reference point. It however is not because by definition it has an undefined space, while a reference point has a defined space. What is similar is that both a reference point, or zero, and infinity both have an undefined value, so then on the number line. ?------(-infinity)------0-------(+infinity)------?. It can clearly be seen how negative infinity has less space, and less value than that of 0, but it of course is undefined, both in value, and space. Where as the positive infinity, is greater than 0 in space and value, but is still undefined, in space and value. So then to bring in Cantor�s ideas of grouping infinity�s, it is represented thusly, and with the understanding that infinites, are in a fashion reference points, they are however not the �original� reference points. I represent this with the following number line. ?------(-0^1)-------------0--------(0^1)---------(0^2)------? Where all the numbers, other than 0 are infinites, they are all referred back to the original, or the �real� reference point of zero. The entire purpose of all this is to unify, and simplify, infinities, and the number line, and zero. With these understanding it becomes much simpler to grasp, what it is to apply and use infinites on the number line along with there relationships with operations. Chapter 10 This is only the beginning of the application of relativity to mathematics. I have so far only applied the idea to basic arithmetic. There has of yet to be a sufficient application of it to the higher tiers of mathematics. I think however that one should already be able to see the benefits and use of relative mathematics. As it will allow us to reduce and simplify the entirety of basic arithmetic. As it will allow for a de-mystification, do to the current systems incompleteness, and allow for a better understanding of pi, and other infinite numbers. With out a doubt I believe that many more ways can be found in which to apply these ideas of relativity. Many of which may be more profound in nature, than the applying of it to basic arithmetic. I think however that the greatest advantage can be found in that of unification of quantum and classical mechanics. It is a fact that currently we find our self in a conundrum as to the unification of the world of quantum mechanics, and classical mechanics. Could it be that the reason is a lack of relativity. That the reason why, we can not merge the two, it is because of a lack of separation in the ideas of the quantities of space, and value. Surely if we are to mix something of gigantic space and value, �classical mechanics�, with something of miniscule space and value, �quantum mechanics�, then without a doubt relatively is the key to its unification. I should have hoped that I have shown how relativity is in fact tailored made for the solving of this issue. It has already shown us that with its application to the number line, it is then possible to grasp wholly the infinitely large numbers, and infinitely small numbers, and there relationship with 0, that are found on any and every number line. Specifically with the physics equations used to merge classical and quantum mechanics. From Michio Kaku himself, the equation that is arrived out of this merger attempt is that of ( A / 0 ). And that with the math of black holes, another merger of classical and quantum mechanics, again the equation arrived at is ( A / 0). This has left physicist baffled, and rightly so. For the current answer for division by zero is undefined, which of course is not an answer. As evidenced by the lack of ability to solve these equations. If however we take into account relativity, we can do something very unique here. If then we say abstractly that A is an infinite, or NEAR infinite number and it is applied to the space of zero, then the answer, instead of A, is A-relative. This is also to say that if A is multiplied by 0 and that A is infinite or near infinite then the answer again is, A relative, and not just A. This is also true of division with infinite, or near infinite numbers. The purpose of this is understood by declaring a definition for what happens with the multiplying and dividing of infinite numbers. I set the following axioms. ( A x 0 = A ) and, ( A / 0 = A ). And that ( 0 x A = 0 ) and ( 0 / A = 0 ) ( A-infinite x 0 = A-relative ). And that ( A-infinite / 0 = A-relative ) To explain these equations with relationships to values and spaces, I assert the following axiom. When a number is infinite, or near it, it is undefined value that is being multiplied or added to zero, but it is greater than zero in value, so it then creates a sum that is defined in value, but undefined in space. That is that it will carry over the undefined space, from the infinite number but the value becomes defined. The reason can be set as an axiom. �All infinite, or near infinite numbers have a value, that is greater in �quantity� (negative is still greater than zero in �quantity�), than zero, even though the value�s for both numbers are undefined.� That is to say that even though a value is undefined, it can still be greater in value than another defined, or undefined value. To say simply any given infinite has more values in them than zero, despite all values being undefined. This then leads me to the totality of this work. What we have then created here is a Relative Number, and it was through the process of a relative equation. I say simply that there are four types of numbers. 1. Reference point or Zero - undefined value, defined space 2. Normal Number- defined value, defined space 3. Infinite Numbers- undefined value, undefined space. 4. Relative Numbers � defined value, undefined space. It will be left to physics to further explore the application of relative numbers, and relative equations, but the need for the application is certainly found in the aforementioned issue of black holes, and the merger of classical and quantum physics. If then undefined values (and tremendously large values) are put into a defined space (no matter how small it is in size even near infinitesimal), such as what happens in these cases, we are then allowed, through relativity, to arrive at a given answer that is acceptable in physics, as well as math. That is to say we can then linguistically explain what happens with black holes. It is then that a defined value is reached, when an infinite or near infinite amount of mass, is put into a defined amount of space, even if minuscule in size. And that because of the newly defined value of the number, and the undefined space, that what we have then is a relative sum. Relative to what it is that we are talking about. Or perform equations for. And in the case of black holes we have all the previously undefined value of A, relatively �added� to a defined amount of space. Giving us then a defined value of A, as we relatively see it, in its undefined space. So linguistically or mathematically, relativity can provide an answer to what is currently unanswerable. As well as unify classical and a quantum mechanics, from the mathematical standpoint. As well as, and least of which is, that relativity can provide a better, more efficient, and simplified version of basic mathematical arithmetic. May 6th, 2013, 05:37 PM #3 Global Moderator   Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms Re: Relative Mathematics Hmm... I only get 30 points on the Caldwell-Baez scale. Does anyone care to break this down into an axiomatic treatment and scrub the philosophical nonsense? There may be something interesting underneath. May 6th, 2013, 05:48 PM #4 Banned Camp   Joined: Aug 2012 Posts: 153 Thanks: 3 Re: Relative Mathematics Thank you for your time, and reply.......name a ancient mathematician that was not FIRST a philosopher. Out of philosophy comes all things. By definition it is the "love of wisdom". I tell you that if I had not have used philosophy, then the merger of 'relativity" between physics and math, would have been much more difficult. But I know that is how you mathematician's like it....so have at it. Just let me know where, and if it's wrong, philosophically of course, I am short on education in regards to complex mathematics. May 6th, 2013, 06:01 PM #5 Banned Camp   Joined: Aug 2012 Posts: 153 Thanks: 3 Re: Relative Mathematics I had never heard of the Caldwell-Baez scale but now that I have done the research I see that you are mocking me. I don't care what you think, of me or my personality. Just the idea. Let us focus on that shall we. Least we turn a Caldwell-Baez scale on you sir. It seems to me that the very idea of the Caldwell-Baez scale is hypocritical. If the purpose is to point out the "crack-pots"....then one must turn there focus from what it is they are saying to the individual themselves. Which seems kinda crack potish to me. If they where a real crack pot just point out the flaws in there paper, not in them. May 6th, 2013, 06:05 PM #6 Global Moderator   Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms Re: Relative Mathematics You posted this on a math forum, so I thought the best way forward would be to extract the mathematics and discuss it. I'm not opposed to a discussion of the philosophy of mathematics (though, strictly speaking, it's off-topic here) but without a clear understanding of the underlying mathematics it would be hard to follow. I assume you're not capable of writing this up as an axiomatic theory (like, say, Peano arithmetic or ZF)? In that case we'll have to hope someone else comes by who is interested and sufficiently motivated to do so on your behalf. May 6th, 2013, 06:13 PM   #7
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Re: Relative Mathematics

Quote:
 Originally Posted by Conway51 Least we turn a Caldwell-Baez scale on you sir.
You should absolutely feel free to do so. Let me also suggest
http://www.scottaaronson.com/blog/?p=304
which is useful for similar purposes. If you find me claiming "revolutionary contributions to physics", making claims about prime numbers, or claiming a mathematical breakthrough it is appropriate for you to apply the relevant scale to judge if what I have written is worth your time (and that of others) to evaluate.

Quote:
 Originally Posted by Conway51 If they where a real crack pot just point out the flaws in there paper, not in them.
The purpose of these three scales is to decide when it's worthwhile to even evaluate the claims seriously. There isn't enough time in the day for me to evaluate all the crackpot proofs in mathematics as they come out, not even if I spent 16 hours a day.

Quote:
 Originally Posted by Conway51 I had never heard of the Caldwell-Baez scale but now that I have done the research I see that you are mocking me.
Hmm... not really. I think that 30 points is a fairly low score, so I suggested that there might be value in what you wrote. If you had scored, say, 100 points I probably would have written, "this guy seems nuts, don't waste your time".

But I do have concerns (thus the positive score). For example, the name-dropping almost made me navigate away from the post -- you refer to Einstein but don't seem to have read his papers. May 6th, 2013, 06:20 PM #8 Banned Camp   Joined: Aug 2012 Posts: 153 Thanks: 3 Re: Relative Mathematics What you say is correct sir. I DO NOT have the education to formally right this is "mathematical" terms. I hope I don't get any points against me for capitalizing my words! It is however in the correct place. It is math. Philosophical math albeit. I would hope, and be ecstatic, if any one (who possessed the education) would apply the effort necessary to write it in the one and only fashion you mathematician's care for. Axiomatically. "There is more than one way to skin a cat." Also I have read in it's entirety "Relativity" written by the man himself. I do not see how you could have jumped to any conclusions as to whether I had or had not read his works. Not that, that even matters. As far as my "Boldness" is concerned.....well I only said what I thought. May 6th, 2013, 06:34 PM   #9
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Re: Relative Mathematics

Quote:
 Originally Posted by Conway51 What you say is correct sir. I DO NOT have the education to formally right this is "mathematical" terms.
So we'll just have to hope that someone who does, and who has the time, happens by this thread. I have the skills but lack the time -- in fact I should not even be posting now...

Quote:
 Originally Posted by Conway51 Also I have read in it's entirety "Relativity" written by the man himself. I do not see how you could have jumped to any conclusions as to whether I had or had not read his works.
I don't see any connection between his work and what you suggest. There's no Euclidean vs. Minkowski signature distinction, no Lorentz factor, not even an analogue of a tensor (of rank > 1). It's possible that these or other elements are hiding underneath your exposition, and I've merely missed them in my cursory scan of your florid writing. But I suspect that the reason I don't see it is because it's not there.

This isn't to say the idea is bad, merely that I don't think it's related to Einstein. May 6th, 2013, 06:45 PM #10 Banned Camp   Joined: Aug 2012 Posts: 153 Thanks: 3 Re: Relative Mathematics Lol....clearly it is you who have not read his works. Space and Time are two things functioning as one. That sir is FACT. I stated clearly that numbers possess this same characteristic.......I was no more florid than was necessary. Further we do not have to wait for someone to "happen" on it. There are 5 doctorates in Amarillo, who currently have this paper. All of which claim...like you....that "something" may be in it. But also like you they don't have the "time". Eventually with the completion of my education maybe I will have the skills required to put this paper in mathematical vernacular.....thank you again for you time. Again and unfortunately....you said nothing of my paper.....only of me. I am of the least importance...the idea is of the most. So to any and all who DO have the mathematical vernacular, and don't mind translating philosophy....have at it. Tags mathematics, relative ,

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# what is the relative about mathematics

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