1. "warning speculation" Relative Mathematics

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.

2. Re: "warning speculation" Relative Mathematics

Hey Conway.

What are you trying to get at? What is the takeaway of your message?

3. Re: "warning speculation" Relative Mathematics

The sum of multiplication and division by zero is relative.
Varying amounts of zero.
A symbolic representation for things of known value, but unknown space.
Defining division by zero.
Clarifying and editing perspectives on current axiomatic arithmetic.

4. Re: "warning speculation" Relative Mathematics

Is this simply an exercise in typing or are you under the impression that you are saying something?

5. Re: "warning speculation" Relative Mathematics

There's an awful lot of axiomatic stuff in there that doesn't represent the world that I live in. Neither does it represent the world of numbers.

Not that you can't make up your own axioms and play with the results, but your efforts tell us nothing about the zero, or the operations with zero that the mathematical world uses.

6. Re: "warning speculation" Relative Mathematics

If my efforts tell us nothing about zero, why then have I defined it as (uv + ds ). I have kept all operations with zero that the world uses, I have only added too those operations. That is (0 * A = 0 ). If any given axiom does not represent the world in which you live, please suggest which axiom, and why. Simply saying you don't agree is not fair. Unless you have no intent of discussing this issue, which would have not required a post. Or at least an insulting, pointless post like HallsofIvy. If then it doesn't represent the world of numbers please suggest a reason why. Are you then suggesting numbers are not a thing? Maybe you feel it is only that they are abstract. Does that then mean abstraction does not have space? Doesn't matter, if ever a number is used to represent a physical thing "ergo mathematical physics", and the things they represent have value and space, then so should the symbol resenting them. I am fine with you not desiring to discuss this.....but help me out, suggest why this is wrong instead of simply making accusations.

7. Re: "warning speculation" Relative Mathematics

Better yet provide not words, only equations. Show me an equation that I can not solve for both * and / by zero, with a sum of both (A) and (0), with out breaking axioms I have given, or axioms currently in existence. (exceptions being zero product property, and division by zero undefined.).

8. Re: "warning speculation" Relative Mathematics

Originally Posted by Conway
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.
I think that all of the above has nothing useful to say to us. Your notion of value is completely vague.

If you want to talk about zero, why not create a theory of numbers rather than something designed for physical objects?

Given that you are focussing on zero and thus numbers, let's address those. They don't have dimensions, so half of your theory is immediately redundant. No number is infinite either. Nor are there any numbers that are inherently large or small. 2 is a small number of fingers for a human, but a large number of heads. 10 is a small number of grains of sugar to have in your coffee, but a large number of sugar cubes to have. A million is small compared to $10^{15}$, but 1 is large compared to $10^{-15}$.

We know how big a number is compared to other numbers without having a label. Your labels don't make sense anyway. A fraction like $\frac94$ is "small", but an integer like 1 is large.

10. Re: "warning speculation" Relative Mathematics

I gave a specific definition for value. It is the labeling of quantity's of existence, other than dimensions. So then wrong or right, it is anything but vague. It is my belief that numbers exist to be applied to physical objects. Not that they have to be, but that it is at the peak of its beauty when it is used for physical objects. Physics would certainly agree. I can think of no "symbol" or "number" that does not possess a dimension. I can measure the width of 1. I can measure the length of the object it is intended to represent. Pie is clearly an infinite number. So then some numbers are infinite. I certainly agree that most of the "further defining" of a defined space or value is not necessary. We know what we are talking about when we observe the symbol used for the number. The purpose of breaking it down in such fashion is important when describing the actions of placing value into space in * and / . Especially when considering infinite(large) values into infinite(small) spaces.

11. Re: "warning speculation" Relative Mathematics

"Space" is not just length and the number 1 has no dimensions. Numbers are mathematical objects and as such can be used to model the real world, but have no direct connection to it. Most of physics is approximation - especially where mathematics is concerned.

It is completely unclear what value there is in labelling $\pi$ as infinite. However, all real numbers are infinite in that sense.

If your idea has much that it necessary, you should dispense to avoid boring or confusing the reader with pointless waffle. The breakdown you give appears to have no function whatever because all aspects are either redundant (all numbers fall into the same category - as in defined and infinite), wrong or contradictory (as in large/small), or included with the value (as in positive or negative).

Infinite(small) spaces means nothing at all to me. There are no infinite spaces in the universe, neither are there infinite values.

12. Re: "warning speculation" Relative Mathematics

Space is the labeling of quantities of dimensions. Any number has a width therefore has a dimension. Abstract or otherwise. As I stated there was a specific point in labeling and "further defining" of quantities of space and value in this specific fashion. I did not mean to imply that it was unnecessary. All numbers do not fall into the same categories. As stated there are four kinds of numbers. Where as no thing that is observable by humans is actually infinite. Many things approach "near" infinite. Especially in physics. If then I have a near infinite or infinite mass and I place it into a black hole (near infinitely small space) then this must be reflected in the equation.

13. Re: "warning speculation" Relative Mathematics

Conway, I looked carefully through your opening spiel, but unfortunately
didn't notice anything that will bring down the price of groceries.

I see you're making others suffer also:
http://www.scienceforums.net/topic/8...e-mathematics/

Plus the "Physics Forum" kicked you out...what a mean bunch...

14. Re: "warning speculation" Relative Mathematics

Originally Posted by Conway
Any number has a width therefore has a dimension. Abstract or otherwise.
Since numbers are abstract, they clearly do not have any dimensions. The only way your description makes any sense at all is if you consider the "width" to be something to do with how the number is written down, but that is dependent on a whole host of factors unrelated to the number itself: the font, the font size, the base, the numerals, etc..

Originally Posted by Conway
approach "near" infinite
This phrase has no meaning at all. Something is either infinite or it is not (as your system says).
A page from Cornell university has the mass of the universe in the region of $3 \times 10^{55} \text{g}$, which (while large) is certainly not infinite. Neither are black holes infinitely small. Our equations in physics do have singularities (and black holes are an example of this) but those singularities are just a sign that the theory breaks down at very small distances. That's why the search is on for a theory of quantum gravity.

15. Re: "warning speculation" Relative Mathematics

I am of the opinion that abstraction posses space. The length of my consciousness is the length of the neurons firing, giving rise to my existence in the first place. A separate debate I suppose. In any case abstraction possessing space does not matter, for reasons already stated. What is or is not infinite is relative to the observer, such as what is small or large is relative to the observer. (.1infinite,.1, 1, 10, 1infinite.). So then if it is or is not relative to my perspective then I can certainly make a statement that it is "near". If then there is multiply universes then the finite number you gave is pointless. As again there would be an infinite number of universes. Look, mathematics does NOT function (except basic arithmetic) without the concept of infinite. Why are we debating the existence of this concept? It is proven and used by mathematicians all the time. I concede that there is not such thing as infinite. Now then to address multiplication and division by zero......

Page 1 of 4 1234 Last