1. Re: Relative Mathematics

Romesk

If you feel I am wasting your time why do you keep replying?

I have been kind and apologetic for my mistakes....the opposite of narcissistic.

If you do not wish to consider the idea I posed then STOP REPLYING...or else you clearly fit the definition of troll.....

You will also find valid reply's in this thread from those who are interested.

Zzephod

Not once has the word gobbledygook been used. Anyone who has "disagreed" with this post, has NOT offered reasons why. Only complaints have been against the failure of the file transfer (fair complaint). And those who actually have valid questions about the validity of the idea. If you feel that it is "gobbledygook".....why?.....would be fair and in order.

2. Re: Relative Mathematics

@Conway:

My response is a little lagging but please make sure you are not talking about what I call "quantities." A quantity is a number (or vector, or tensor, etc.) with unit. For example, we may have 4 apples...number = 4 with the unit "apples." Note that you can't multiply the two quantities 4 apples by 3 apples as 12 apples^2 has no meaning. So within your structure you and I may be fine. (At least for the moment. Your detractors are making good points.)

-Dan

3. Re: Relative Mathematics

Dan

I am not talking about quantities as you are. I am not applying UNITS of any kind. As I posted the idea is technically held only to pure mathematics. Also I agree my detractors are making good points. I have acknowledged them and apologized. But none of them have made any contrary points regarding the nature of the idea. Only to say that it is hogwash, and gobbbledegook, without suggesting why. I hope you wish to continue. In the original post I offered definitions for value and for space.

space = labeling of quantities of dimensions
value = labeling of quantities of existence other than dimensions

you of course can see how this would "in the end" effect ideas such as units. If then we declare a separation in the symbolic representation of a "Number" between space and value, it would then make units as we conceive them to be unnecessary, as the given "unit" would be declared the value, while the space is the quantity of dimension it occupies.

Romsek, Zzephod

I hear you, I appreciate you, I understand you. It would seem no further communication between us is necessary or valid.

Sincerely I thank you,

conway

4. Re: Relative Mathematics

If you can tell us how to make it consistent then it will make more sense to the readers.

If not it is basically just a bunch of random words thrown together.

5. Re: Relative Mathematics

Chiro

Thank you for this advice...I will attempt to do that now

When A is used as value and multiplied by zero as space then the sum is A
When 0 is used as value and multiplied by A as space the sum is 0

A(as value, or z1) x 0 (as space, or z2) = A
0(as value, or z1) x A (as space, or z2) = 0

I hope I have done as you requested

6. Re: Relative Mathematics

Originally Posted by Conway
When A is used as value and multiplied by zero as space then the sum is A
When 0 is used as value and multiplied by A as space the sum is 0
I'm going to echo what someone else asked: What do you mean by "sum" here?

-Dan

7. Re: Relative Mathematics

Dan

Valid question, thank you

all symbols on the left of the equal sign are composites of numbers. That is a space and a value separately.

all symbols on the right of the equal sign (the sum) are a full fledged number containing both value and space not separated.

In the op, I stated that it is that a value is placed into a space there by generating a number.....for multiplication....and division....slightly more to it then that, we can get there latter if you wish.

8. Re: Relative Mathematics

Originally Posted by Conway
Dan

Valid question, thank you

all symbols on the left of the equal sign are composites of numbers. That is a space and a value separately.

all symbols on the right of the equal sign (the sum) are a full fledged number containing both value and space not separated.

In the op, I stated that it is that a value is placed into a space there by generating a number.....for multiplication....and division....slightly more to it then that, we can get there latter if you wish.
Okay, you are apparently using symbols and terms in unusual ways. If I may, please let me suggest some notation.
Definition: Let the ordered pair (v,s) be defined in the following way: $\displaystyle ( ~, ~ ) : V \times S \to Q: \forall v, ~s \in V, ~S \mapsto (v,s) \in Q$
where V, S, and Q are "value," "space," and "quantity" spaces.

Then we have some defining properties (A, 0) = A, (0, A) = 0, etc. It's still not great, as A in Q space still looks like A in V space, but I think it's a bit better. (Perhaps even $\displaystyle (A, 0) = A_Q$?)

Just a thought.

-Dan

9. Re: Relative Mathematics

Dan

I would love to use notation. I am very weak in such matters (set theory). I however have done some research on the symbols used in order to better understand you at this point. I hope you will bare with me as we continue along these lines. Please note I will post nothing of "certainty" until you have helped me understand. As far as the notation you used....can you explain more about why you chose Q. What is it that you mean by "quantity space" as opposed to "space". I will await more from you on this matter before I "judge" the notations that you gave. Until then I pose the following notations.

Where V = value, S = space, A = any number in the Set

let the ordered pair (V,S) be described as follows

(V + S) → A: ∀A, S ∈ V, S→(V,S) ∈ A, V ∈ S, V→(V,S) ∈ A
∀A ≠ 0: (V,S) = (A,A)
∀A = 0: (V,S) = (0,1)

Or alternatively

(V,S) ∈ ∀A
∀A ≠ 0 : (V,S) = (A,A)
∀A = 0 : (V,S) = (0,1)

?????What do you think????

10. Re: Relative Mathematics

Originally Posted by Conway
Dan

I would love to use notation. I am very weak in such matters (set theory). I however have done some research on the symbols used in order to better understand you at this point. I hope you will bare with me as we continue along these lines. Please note I will post nothing of "certainty" until you have helped me understand. As far as the notation you used....can you explain more about why you chose Q. What is it that you mean by "quantity space" as opposed to "space". I will await more from you on this matter before I "judge" the notations that you gave. Until then I pose the following notations.

Where V = value, S = space, A = any number in the Set

let the ordered pair (V,S) be described as follows

(V + S) → A: ∀A, S ∈ V, S→(V,S) ∈ A, V ∈ S, V→(V,S) ∈ A
∀A ≠ 0: (V,S) = (A,A)
∀A = 0: (V,S) = (0,1)

Or alternatively

(V,S) ∈ ∀A
∀A ≠ 0 : (V,S) = (A,A)
∀A = 0 : (V,S) = (0,1)

?????What do you think????
If I am understanding you what you want is a notation to make a difference between values (V) and space (S). I chose the ordered pair notation to avoid the "+" notation: You are adding value and space and they are not the same kind of thing. So the addition is potentially screwing up your meanings. I mean, how can you add 3 + apples? One is a (numeric) value and the other is your space. But we can easily say that we have (3, apple). Do you see what I mean?

I admit that I am still not quite in order with your concepts. I was writing the (3, apple) = 3 apples. I know that's not precisely what you are trying to say but am I right in saying that (3 + apples) lives in neither V nor S? I was calling that a "quantity," hence it belongs to a new set Q . I was also trying to use a convention where the elements of V (value) would be in lower case letters to distinguish it from the set V. So $\displaystyle v \in V$. It makes element vs. set a bit easier to read.

As far as your definitions are concerned:
1. (V,S) ∈ ∀A. Are you trying to say that all elements in both V and S are drawn from a set A? Or is A a specific member of V and S?

2. ∀A ≠ 0 : (V,S) = (A,A). Again with the all values question. Are you saying that (V, S) = (A, A) for any members of V and S?

3. ∀A = 0 : (V,S) = (0,1). What are 0 and 1 representing here?

-Dan

11. Re: Relative Mathematics

Dan

I will listen carefully to you, so as to learn. I understand what you are saying regarding (3 + apples). As long as we are agreed that 3 is not the numeric representation, but rather the space. So too apples is not the numeric representation but the value. When value is (+) to a space then a "numeric" value is created. This is why I have not heavily invested in notation. As neither V nor S (as I use them are sets.) I will switch to (v,s) as you suggested. I understand and agree that distinguishing elements from a set is necessary. I would like to say here...no matter the SET, all elements there in contain a (v,s). That is value and space are property's of all elements in any given set. I use A as (any number in any set). As to your numerical points

1. Yes (v and s) are drawn, or elements of A (any number in any set).
2. Yes (v, s) are members of all elements of any set.
3. (0,1) is the equivalent to (v,s) for the element 0 that belongs to a set.

Allow for the following

1(as a number) is composed of (v,s) = (1v,1s) = (1,1). The "numbers" in the parenthesis are not numerical.
(_) = one space, no value
(1) = one value, no space
(1) = one value added to one space = 1 (a number)

2(v) X 3(s)

(2(as value) is placed into 3(as space))

(_,_,_) three as space only
(1,1) two as value only, alternatively (2)

(2+2+2) value of two placed into three spaces

note the (+) comes from the axiom of multiplication when value is "placed" into space.

so then with 1 and 0

0 as value only = (0)
0 as space only = (_)

1 as value only = (1)
1 as space only = (_)

The space of zero is equivalent to the space of one, the difference is in 1 having a single defined value, where as 0 has a single undefined value.

12. Re: Relative Mathematics

Hey Conway.

When you combine different objects you need some sort of rule to combine them.

The two main structures in mathematics are numbers and sets and you use arithmetic to combine numbers [and synthetic structures like vectors] and you use set intersections and unions for sets.

Can you express the algebra [i.e. way of combining them] with one or both of these structures? [This is as general as it really gets for current mathematics]

13. Re: Relative Mathematics

One reason that you get a bad reaction from your suggestion is that what you are saying is muddled from the start.

Originally Posted by Conway
It is the inherent nature of all things thatthey are a compilation of two different and distinct things. It is axiomaticthat these two things are space and value.
It may be axiomatic to you, but it isn't an axiom that the majority can by into without some justification which you fail to give. On the other hand, if you are just setting up a (new) number system, you should say so without the psuedo-philosophical mumbo-jumbo. Just state what the system consists of: ordered pairs (a,b) with operations that do whatever it is they do.

14. Re: Relative Mathematics

Chiro

The combining of value and space are done so with the axioms of multiplication and division. As given in the op.

Multiplication = The value given is placed equally into the spaces given, then all values are added in all spaces.
Division = The value given is subtracted equally into all spaces given. Then all values and all spaces are subtracted but one.(inverse of multiplication)

Archie

I am not setting up a new number system. I have only....

Redefined numbers (within the CURRENT system). I have done so using axioms. You either agree or you don't. I would love to discuss the validity of these axioms, but that would require more of that "mumbo-jumbo". With the redefining of what a number is...a single field axiom can be written to allow for division by zero. Allow for multiplication by zero with sums other than zero. Allow for varying amounts of zero.

Thank Again Archie for you time.

15. Re: Relative Mathematics

Originally Posted by Conway
I am not setting up a new number system. I have only....

Redefined numbers (within the CURRENT system).
That is creating a new system. Numbers in are defined in the current system and the way they are defined is nothing like what you are writing.

The problem is that you say what you are doing is pure maths (i.e. set up some rules and follow them) which is fine, but then you try to say that it is the existing system of maths. That simply can't be because the current system is different to what you are proposing.

On the other hand, you talk about the validity of your axioms. Axioms don't have to be valid, they just are. But if you are claiming that your system is a better model for reality than the existing standard system, you have to justify your axioms.

Pure maths: just state your axioms in a mathematically precise way without grandiose claims about relevance to the real world and start proving stuff.
Applied maths/physics: justify why your axioms are a better model for the real world than the current system. Then proceed as for pure maths.

The existing mathematical system has no need of an ability do divide by zero. In fact, the inability to divide by zero is integral to the proper functioning of the system.

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