Relative Mathematics
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4/30/2015 6:52:07 PM Posted: 2 years ago Relative Mathematics
It is the inherent nature of all things that they are a compilation of two different and distinct things. It is axiomatic that these two things are space and value. The value of any given thing being what it is, while the space is what it occupies. It is true that, abstract or otherwise numbers are a thing, therefore they must also contain a compilation of space and value. It is an axiomatic truth that space is the labeling of quantities of dimensions. It is an axiomatic truth that value is the labeling of quantities of existence, other than dimensions. It is an axiomatic truth that space and value exist in one of two forms. So that any given quantity of space or value is first labeled as defined or undefined. It is reasonable to say that any given number, that has had both its quantities of space and value labeled as undefined, requires no further question as to its nature. If however a given number, has had both its quantities of space and value labeled as defined, it is then necessary to further define the given quantities. That is to say what is the nature of the space and value's that are defined. There are four axiomatic steps in the further defining of a defined quantity of space and value. First it is that, after a given quantity of space and value is labeled as defined, a symbol is given to identify the amount of quantities given. Second it is that the given amounts of defined space and value are labeled as finite or infinite. Third it is that the given amounts of defined space and value, that are finite or infinite, are labeled as small or large. Fourth it is that the given amounts of defined space and value, that are finite or infinite, small or large, are labeled as positive or negative. It is the case that all forms of the defining of quantities of space and value, are from the perspective of our humanity. This then shows that there is a collection of only four kinds of numbers. That is there are numbers that possess an undefined space and an undefined value. Otherwise represented as a ( Uv + Us ). Such a number not requiring further defining. There are numbers that possess a defined value and a defined space. Otherwise represented as a ( Dv + Ds ). Such a number requiring further defining. There are numbers that possess a defined value and an undefined space. Otherwise represented as a ( Dv + Us ). There are numbers that possess an undefined value and a defined space. Otherwise represented as a ( Uv + Ds ). It is reasonable to say that natural numbers have both their quantities of space and value labeled as defined. That is that a natural number is a ( Dv + Ds ). It is then through the process of further defining, that a natural number such as 2 is labeled as having ( 2Dv + 2Ds ). The symbol 2 then is the symbol identifying the amounts of quantities contained. It is then that the given quantities are labeled as finite. Otherwise represented as a ( 2DvF + 2DsF ). It is then that the given quantities are labeled as large. Otherwise represented as a ( 2DvFL + 2DsFL ). It is then that a positive is assigned to the compilation of space and value, and it is so on for any natural number. It is also the case that fractions are labeled as a ( Dv + Ds ). That is any given fraction has both its quantities of space and value labeled as defined. So that such a number as .2 is labeled as ( 2DvFS + 2DsFS ). Then a positive is assigned to the compilation of space and value. Additionally a fractional symbol may replace the decimal symbol. It is also the case that infinite numbers are labeled as a ( Dv + Ds ). So that such a number as 2infinite is defined as a ( 2DvIL + 2DsIL ). As well as fractional infinites such as .2infinite. Which is labeled as ( 2DvIS + 2DsIS ). Then a positive is assigned to both compilations of space and value, and it is so on for any infinite or fractionally infinite number. Remaining are numbers that are a ( Uv + Ds ) and numbers that are a ( Dv + Us ). Such numbers do not necessarily require further defining. As an undefined quantity of space or value composites the given number. So then such numbers can only be limitedly defined relative to the given defined quantity. If then a number possess a defined value and an undefined space, the sum is then relative to the defined value. So that such a number as ( Dv + Us ) is then a 1 relative. Otherwise represented as a 1r. If then a number possess an undefined value and a defined space, the sum is then relative to the defined space. So that such a number as a ( Uv + Ds ) is then a zero. As no quantity of value is defined, and as one quantity of space is defined. The space of zero is clearly defined on any number line. The equation ( 1 + (1) = 0 ) proves this in that, if zero did not occupy a defined space on the number line, then the equation would equal ( 1 ), and not zero. It is the case in multiplication and division, that neither number given is an actual number. Not in the fashion that each symbol contains both space and value. It is that one symbol is representing a value, and that one symbol is representing a space. It is the case that in multiplication the labeling of the given symbols as space or value in a specific order is not necessary. The sum yielded is always the same. It is the case that in division the labeling of the given symbols as space or value in a specific order changes the sum that is yielded. So that as an axiom the first given symbol is labeled as value, while the second given symbol is labeled as space. It is then that in multiplication the given value is placed additionally into the given spaces. Then all values are added in all spaces. It is then that in division the given value is placed divisionally into all given spaces. Then all values are subtracted except one. So that in the equation ( 2 x 0 = X ), there is a given defined value of ( 2DvFL ), that is placed additionally into the given defined space of ( Ds ). Then all values are added in all spaces. This process then yields the number 2. Where as the equation ( 0 x 2 = X ), there is a given undefined value of ( Uv ), that is placed additionally into the defined space of ( 2DsFL ). Then all values are added in all spaces. This process then yields the number zero. So then in the equation ( 2 / 0 = X ), there is a defined value of ( 2DvFL ), that is placed divisionally into the defined space of ( Ds ). Then all values are subtracted except one. This process then yields the number 2. Where as the equation ( 0 / 2 = X ), there is an undefined value of ( Uv ), that is placed divisionally into the defined space of ( 2DsFL ). Then all values are subtracted except one. This process then yields the number zero. It is possible that further defining of the given defined value of a relative number, and the given defined space of a zero, is applicable and necessary. 
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4/30/2015 7:35:00 PM Posted: 2 years ago At 4/30/2015 6:52:07 PM, Philostotle wrote:I find myself being comprised entirely of nose and notnose, for example. There's a lot more notnose than nose, which seems arbitrary to me. I'm working on growing more nose by snorting penisenlargement powders, while reducing the notnose as much as I can, through (for example) haircuts, fasting and tighter waistbands. It is axiomatic that these two things are space and value.The value in this case, being my nose, which gets everywhere first, while most of my space is occupied by notnose. I was following you to this point, Philo, but I'm afraid you lost me after that. :( 
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4/30/2015 10:43:09 PM Posted: 2 years ago At 4/30/2015 6:52:07 PM, Philostotle wrote: What the math did I just read? At points it sounds a little like you're trying to describe vector spaces or vectors in affine spaces, but most of it just looks completely arbitrary. You jump between implicit presuppositions of being in real space and integer space, for example, and I don't think you've described multiplication or division accurately in any geometry. Can you clarify what you are trying to express with this? 
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5/5/2015 12:38:49 PM Posted: 2 years ago I have changed nothing with multiplication or division, other than in regards to Zero and its relationships to the operations. I am trying to express a more accurate description of real tangible mathematics and the theoretical construct of mathematics. It would at first seem arbitrary, If you were however to perform several basic operations on the axioms I have given, you would soon see the necessity. Theoretically. Also I would suggest a great use of relative mathematics by the field of quantum mechanics. What is a particle in the state of superposition if not a relative number. Clearly defined value, occupying and undefined space.

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5/6/2015 8:20:51 AM Posted: 2 years ago At 5/5/2015 12:38:49 PM, Philostotle wrote: Okay, so the natural number 2 is defined as ( 2DvF + 2DsF ) However, in your definition, you use natural numbers in your definition of the natural number; so this actually becomes: ( ( 2DvF + 2DsF )DvF + ( 2DvF + 2DsF )DsF ) In this further clarification, you continue to use natural numbers, however so this can be further defined as : ( ( ( 2DvF + 2DsF )DvF + ( 2DvF + 2DsF )DsF )DvF + ( ( 2DvF + 2DsF )DvF + ( 2DvF + 2DsF )DsF )DsF ) The only meaningful resolution in this respect, is to assign a value of 1 to DvF, and 0 to DsF, which yeilds the following value for the set of infinite terms: 2 = 2 
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5/6/2015 8:47:27 AM Posted: 2 years ago If read in its entirety you will see a natural number contains a total of four pieces of information. That is that a natural number is (2dvfl + 2dsfl) not (2dvf ). Further I offered a definition of all forms of numbers not just natural. And I offered axioms for the definition of a natural number. This is not the same as defining something with the name of the thing itself. This is anything but circular logic. In any case one can not multiply values and spaces as you suggest in your equations. Numbers yes, but not values and spaces. Values are placed into spaces, then operated on.

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5/6/2015 10:05:07 AM Posted: 2 years ago At 4/30/2015 6:52:07 PM, Philostotle wrote: All I know is that 1 is the only true number that exists. Everything else came from that 1. Without that 1, 2 wouldn't exist. 0 is meaningless therefore it doesn't really exist in 1 but it can be used to stop 1 long enough to cause information to exist such as the case in computer binary code. If everything was 1 in computer binary code, no information would exist, it would just be 1. 
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5/6/2015 6:05:01 PM Posted: 2 years ago Zero is not meaningless. If it were, why would it exist in binary. If zero did not exist, then why can I use it at all. Such as you yourself suggested. Zero is space, with undefined value. Cleary then it is not nothing, therefore it is something, therefore it exist. Zero by current mathematical definition belongs to the "whole number" category. Therefore it is a number.

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5/6/2015 8:33:10 PM Posted: 2 years ago At 5/6/2015 6:05:01 PM, Philostotle wrote: 1+0 = 1 1x0 = 1 1divided by 0 = 1 1x1 = 1 2+0 = 2 2x0 = 2 2 divided by 0 = 2 0+0 = 0 I can't seem to get 0 to work as a number. 
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5/6/2015 8:36:07 PM Posted: 2 years ago At 5/6/2015 6:05:01 PM, Philostotle wrote:Philo, do you know that you can capture number theory algebraically, without geometry? You can: such work is over a century old, and begins with the work of Charles Sanders Peirce, Richard Dedekind and Giuseppe Peano. They and their successors showed you don't need a field full of sheep (say) or a bucket full of marbles to define arithmetic. You just need a symbol  call it 'zero'  a simple counting function called 'next' which can apply to zero or itself, and some basic algebra: rules for defining new operators such as 'add' and 'subtract' and 'multiply' in terms of zero and 'next'. That plus some logic gives you arithmetic. Mathematicians use numbers in geometry, but there are good reasons they don't do the reverse. One is that algebra works really, really well for numbers already. Another is that certain mathematical domains have no intrinsic notion of space: algebra itself and statistics, for example. A third is that algebra is somehow more fundamental than numbers or geometry  so we're better off defining each algebraically than defining either in terms of the other. So combining defining numbers in terms of geometry seems a curio at best: like defining a wheel as a hedgehog wrapped around a wooden log. A bit of contemplation will tell you that you probably don't need the hedgehog, and that regardless, we already have very good wheels. :) I hope that helps. :) 
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5/6/2015 8:54:19 PM Posted: 2 years ago The 0 used in binary code isn't used as a number. It is used as a variable to convert thoughts from the mind into other kinds of information that is processed through a computer processor.
The 0 we use in the decimal system acts as the number 10 but we don't use the number 10 in the decimal system such as 1.10. 1.10 is the same exact thing as 1.1 The 0 in 1.01 is one and onehundredth of another 1. Do you see how 0 is representing 10 and not 0 as a number? 
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5/6/2015 10:14:13 PM Posted: 2 years ago baddebater
neither myself nor anyone else claimed that zero was the equivalent to a place holder. Your point was not congruent with anything said. RuvDraba I have at no time talked of geometry. The words I have used are space, and value. One can not write a number with out the use abstract or otherwise to the two. Further, as I mentioned in the original post, all things contain space, and value. Whether geometry or otherwise. I am re constructing basic axiomatic arithmetic, not geometry. Additionally in such a way as to not effect, change, or alter, any other branch of mathematics whatsoever, insofar as they are related to operations by zero. 
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5/6/2015 10:20:33 PM Posted: 2 years ago baddebater
I can not say if zero is considered a number in regards to binary. I therefore defer to your truth that it is not. I however, am not talking about the zero of binary. Additionally it still remains that zero, as used in binary, is not meaningless or non existence, otherwise it would not be used at all, as was my point in that post. 
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5/6/2015 10:41:03 PM Posted: 2 years ago At 5/6/2015 10:14:13 PM, Philostotle wrote:My original statement; 0 is meaningless therefore it doesn't really exist in 1 but it can be used to stop 1 long enough to cause information to exist such as the case in computer binary code. My original statement was meant to say that zero doesn't have any meaning when it comes to being a number. It is used for other reasons than a true number such as a variable to make computer binary code work. Without a change from a 0 to a 1, there wouldn't be any conversion of information from thoughts to information that we can experience through computer peripherals. If binary code read; 111111111111.......... thoughts couldn't be converted into other kinds of information. RuvDraba 
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5/6/2015 10:47:20 PM Posted: 2 years ago At 5/6/2015 10:20:33 PM, Philostotle wrote: I don't think you understood me when I made that statement about 0 being meaningless. It is meaningless as a real number but it does have it's place as far as what we use it for in mathematics and computer binary code. For example, when we count, we think that to make "one", we have to start at zero. But everything came from one, not zero. Zero is nothing so it's impossible that one came from nothing. 
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5/6/2015 11:11:33 PM Posted: 2 years ago As I see it, it is that nothing does not exist. It is the very definition of itself. Now clearly a concept of no concepts exists, but the concept itself is something. What the concept is of, does not. This is all to say, that no where can you point and say, There! There! is nothing. Because it does not exist. Zero exist. I can point to it. It is not nothing. It is space with undefined value. But it is not noting.

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5/7/2015 8:05:15 AM Posted: 2 years ago At 5/6/2015 11:11:33 PM, Philostotle wrote: Can you define space without any objects to observe or measure. Does information require space to exist? 
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5/7/2015 7:20:26 PM Posted: 2 years ago One can measure any space empty or otherwise. I offered a definition of space with out objects or measurements. That is to say space in the labeling of quantities of dimensions. While value is labeling of quantities of existence other than dimensions. Information with out space then is essential the definition of value. Though as I have already stated, there is not nothing. Therefore space is everywhere. Therefore no idea can exist without containing a measure of space. It is possible to reduce and abstractly use only one or the other.

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5/7/2015 7:25:22 PM Posted: 2 years ago At 5/6/2015 10:14:13 PM, Philostotle wrote: I think it would be easier to understand if you wrote this out formally rather than like a philosophical essay. It's unclear otherwise. A question: How are Peano's axioms reformulated in this new framework you're proposing? 
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5/7/2015 7:35:53 PM Posted: 2 years ago There is nothing informal about my paper. It is NOT mathematics. It is philosophy. That is why mathematicians do not like it. That is why you feel it important that it be more akin to mathematical papers, such as proof and the like. There are not proofs to write. There are no equations to show. Even what appears as equations in my paper are not really. Each and every sentence was clearly constructed back to back as axioms. Either you agree step by step, or you do not. Asking what anything times anything is, is math. Asking why it is, is philosophy. I am not asking what anything times anything is, I am only asking why it is. Ask a scientist to tell why a electro magnetic field is, he can not say, he can only say what it is, and what it does.

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5/7/2015 7:42:31 PM Posted: 2 years ago At 5/7/2015 7:35:53 PM, Philostotle wrote: Are you familiar with how axioms are normally written? I am still not clear on what the goal, purpose, or point of your original post is. 
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5/7/2015 7:45:34 PM Posted: 2 years ago Peano Axioms is a set of axioms following from a given set of natural numbers, of which zero is considered to be a natural. This is well and good, but we are not talking about a set. Unless you consider it to be the "uber" set. A set of all numbers finite and infinite. Peano's set was ONLY naturals. His axioms are great see....as long as you stick with only natural numbers. It all falls apart applying infinites. Which as we know clearly exist.

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5/7/2015 7:50:40 PM Posted: 2 years ago If mankind always stuck to normality, then what a bore we would be. An axiom is defined as a self evident truth. Each sentence as stated is such. Also the goal, expression, as previously stated, is to redefine basic arithmetic to match physical reality, as well as provide unification for quantum and classical mechanics. Alegedly....in any case to provide a more accurate form of mathematics. Relative Mathematics leaves no equations undefined.

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5/8/2015 2:40:27 AM Posted: 2 years ago At 5/7/2015 7:20:26 PM, Philostotle wrote: It's impossible to define space without any objects in it. We simply don't have the convenience of empty space to understand this. 
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5/8/2015 8:03:36 AM Posted: 2 years ago At 5/6/2015 8:33:10 PM, baddebater wrote:At 5/6/2015 6:05:01 PM, Philostotle wrote: Who taught you basic arithmetic? Fatihah: It's like your mother making spaghetti and after you taste it and don't like it, you say "well my mom must not exist". Not because their is no logical evidence but because she doesn't do what you want. 
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5/8/2015 11:52:44 AM Posted: 2 years ago At 5/8/2015 8:03:36 AM, deeem wrote:At 5/6/2015 8:33:10 PM, baddebater wrote:At 5/6/2015 6:05:01 PM, Philostotle wrote: I'm the teacher. Are you going to be my student? 
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5/8/2015 4:31:10 PM Posted: 2 years ago Space is the labeling of quantities of dimensions. I defined it with out measuring it, or asking if anything was "in" it or not. Not a single equation you wrote was mine. Look at the poster please. It is however what I am claiming, short of the inverse equation's related to zero. I do not mine being a student, I know I have more to learn, I do not mind that you are the teacher, all men have wisdom of some measure. Posting things emotionally, and off topic are not very nice. Additionally you appear to be rereading older post, which means either A, you can't stay on topic, B, you haven't actually fully read any of the post, or C, you just like passive aggressiveness. In any case thank you for your time.

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5/8/2015 4:36:03 PM Posted: 2 years ago At 5/8/2015 4:31:10 PM, Philostotle wrote: You didn't define space at all. You were only defining what you believe to be true. 
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5/8/2015 4:40:37 PM Posted: 2 years ago And I believe it to be true that space is defined thusly.

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5/8/2015 4:46:49 PM Posted: 2 years ago At 5/8/2015 4:40:37 PM, Philostotle wrote: Belief is a very powerful thing and I'm certainly not here to change your beliefs. Your space is much different than mine. 