1. ## Re: Relative Mathematics

Archie

Thank you.

I however have already done as you asked. I posed 1 simple field axiom to be taken as an addition to all current field axiom. The nature of which will allow for division by zero (among other things). It does so with out changing ANY OTHER axiom. Therefore I have altered the definition of a "number" with-in the current system without changing the current system. It can only be said that there is a "failure" in the current system with division by zero. It can not be said that it is "ITERGRAL to the proper functioning of the system". It's that the system can not do it. Except the Riemann Sphere, where division by zero finds meaning.

Also I would disagree with your very first statement. Numbers are already defined exactly as I am posing. It is only that I have made a clear distinction between a "numbers" pieces, where mathematics has currently not.

I look forward do more of your thoughts.

2. ## Re: Relative Mathematics

It's not specific enough for me Conway.

You should specify some set theoretic definitions and/or definitions with numeric structures [like linear objects in some field].

You can't rely on vague notions and vague means that you can't put it in specific terms.

Remember - the algebra involves intersections and unions for sets and arithmetic for everything else.

If you can explain this [and do so specifically without using convoluted language] then you will get the point across.

Specifics Conway - more specifics.

3. ## Re: Relative Mathematics

Chiro

I understand you, I appreciate you. You feel that I was/am not specific enough. If I may say one last thing as we part ways....

Leave all "theoretic definitions and/or definitions with numeric structures [like linear objects in some field", exactly as they are.

I have stated things that only affect multiplication and division by zero. All other multiplication and division yields their current sums......so unless you are using liner objects that are related to zero (which your not), then there is not a problem with what you are posing is a problem......

Also one can not get more specific then a field axiom...maybe you should apply my field axiom to some "linear object in some field".

Sincerely thank you for your time.

Conway

4. ## Re: Relative Mathematics

I'll make this as easy to understand as possible.

There are two main structures in mathematics - numbers and sets.

Sets have two main operations [and they can be related to one another] which are intersections and unions.

Example - A and B or A or B.

Numbers have five main operations - addition, subtraction, multiplication, division and the modulus.

Can you tell me what structure you are using and what operations in terms of the AND, OR, +, -, *, /, and MOD?

If you can't do that then nobody will understand you.

Also - if you are using numbers then you will run into problems with zero's which means it's highly likely that you are using sets and if so you will need to describe what operations you are using in terms of the unions and intersections of sets.

It's very simple to do the above.

5. ## Re: Relative Mathematics

Chiro

I think I see where our problem has been.

I am NOT using sets
I am NOT using numbers

I am using composites of numbers...for example

(_) = one space = z2
(1) = one value = z1

when a value (z1) is "placed" into a space (z2) a number is created.

in a binary operation of multiplication or division one symbol represents z1, and the other symbol represents z2.

2 x 3

2(value,z1) x 3(space,z2)

(_,_,_) = three spaces
(1,1) = 2 values, or alternatively (2)

I place the values into the spaces.....then add

(1,1+1,1+1,1)...or alternatively (2 + 2 + 2)

After and only After placing value into spaces do I arrive at a number.

I hope here you can see...I am not using numbers....Nor am I using sets.....I am using pieces of numbers.

Thanks...

6. ## Re: Relative Mathematics

Originally Posted by Conway
Chiro

I think I see where our problem has been.

I am NOT using sets
I am NOT using numbers

I am using composites of numbers...for example

(_) = one space = z2
(1) = one value = z1

when a value (z1) is "placed" into a space (z2) a number is created.

in a binary operation of multiplication or division one symbol represents z1, and the other symbol represents z2.

2 x 3

2(value,z1) x 3(space,z2)

(_,_,_) = three spaces
(1,1) = 2 values, or alternatively (2)

I place the values into the spaces.....then add

(1,1+1,1+1,1)...or alternatively (2 + 2 + 2)

After and only After placing value into spaces do I arrive at a number.

I hope here you can see...I am not using numbers....Nor am I using sets.....I am using pieces of numbers.

Thanks...
I'm totally lost. You need to get to the very basics here. What are "pieces of numbers" and how do you combine them to become numbers. Be specific and give examples where you can.

-Dan

7. ## Re: Relative Mathematics

Dan

Of course, I understand your request here.

The pieces of a number are

Value
Space

A value is placed into a space to create a number

(_) = one space
(1) = one value
(1) = 1 (the number)

Did you read post #26....I felt we may have been close to an understanding at this point.....I am more than willing to return to notation.....albeit it presents difficulty

Better? If not.... I understand if you no longer wish to continue. I certainly hope this is not the case.

8. ## Re: Relative Mathematics

Everything should be isomorphic to a set or number in some way.

Numbers are sets with specific organization [i.e. they organize information so that arithmetic and geometry make sense].

If you can't represent what you are doing with some sort of set structure and algebra then you aren't doing mathematics.

9. ## Re: Relative Mathematics

Chiro

I can and have, though much work has to be done in this regard. Please refer to post #27.....ill copy and paste the relevant parts for you actually.....

(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)

V= value, or z1
S= space, or z2
A= any number in a given set

10. ## Re: Relative Mathematics

How do you construct the mappings in terms of set unions and intersections?

11. ## Re: Relative Mathematics

If you divide an object into pieces, you can't just assume that you keep all the previous axioms without introducing contradictions, you have to show it. Your axioms ought to be written in terms of the most basic building blocks of the system.

12. ## Re: Relative Mathematics

Originally Posted by Archie
If you divide an object into pieces, you can't just assume that you keep all the previous axioms without introducing contradictions, you have to show it. Your axioms ought to be written in terms of the most basic building blocks of the system.
Since you have gone down this route I think I will throw the Banach-Tarski paradox into the mix. A rather nice video on it can be found here on YouTube:

13. ## Re: Relative Mathematics

Chiro, Dan, Archie

I think I finally understand the mistake I have been making. I have spent the last several hours trying to find a solution to Chiro and Dan's last few post. I believe I might have done so...

A = any number
S = any set

Let the ordered pair (x,y) be described as follows...

((z1,z2),(z1,z2)) → (x,y) : ∀A in S

∀A ≠ 0: (z1,z2) = (A,A) = A
∀A = 0: (z1,z2) = (0,1) = 0

combined with the axiom

"Any A in binary operation of multiplication or division is only representing z1, or z2."

If this is worse not better, than I am forced to concede to the forum members. Only in order to continue my education in this regard. I sincerely hope however a few members might be willing to help me continue to "concrete" this idea.

Also I would ask permission from Dan, to post a new topic extolling the virtue's of the members of this forum, regarding this EXCELLENT peer review.

Sincerely Conway

14. ## Re: Relative Mathematics

Originally Posted by Conway
Chiro, Dan, Archie

I think I finally understand the mistake I have been making. I have spent the last several hours trying to find a solution to Chiro and Dan's last few post. I believe I might have done so...

A = any number
S = any set

Let the ordered pair (x,y) be described as follows...

((z1,z2),(z1,z2)) → (x,y) : ∀A in S

∀A ≠ 0: (z1,z2) = (A,A) = A
∀A = 0: (z1,z2) = (0,1) = 0

combined with the axiom

"Any A in binary operation of multiplication or division is only representing z1, or z2."
Again we have confusion. I can see what you might be trying to reach for but you still aren't defining the "major players" all that well.

For example: $( ( z_1 , z_2 ) , ( z_1, z_2 ) ) \to (x, y)$. What are z1 and z2? Would they be members of a set that you haven't mentioned yet? And how can $( z_1 , z_2 ) = x$ and $( z_1 , z_2 ) = y$ at the same time if x and y aren't the same?

Also I would ask permission from Dan, to post a new topic extolling the virtue's of the members of this forum, regarding this EXCELLENT peer review.
Sure! We always like good feedback. But please put the thread in the Feedback Forum. (And you don't need my permission to post anything so long as it conforms to the Forum Rules below.)

-Dan

15. ## Re: Relative Mathematics

Dan

(z1,z2), are not members of any set...(they be considered pieces of the members of the set)

They are

z1=value
z2=space

"z1 and z2 for A, (any number) is "really" just the number given put into what appears to be an order pair"

z1,z2 for A = (A,A)
z1,z2 for x = (x,x)
z1,z2 for y = (y,y)
z1,z2 for 2 = (2,2)
z1,z2 for 3 = (3,3)

Any number has the same quantity of space, as it has value......except zero.

(_)= one ACTUAL space, no value = z2
(1)= one value, no space = z1

If I put these things together I get a number

(1) = 1

If you "think" you may be seeing what I am reaching for... I will continue....please let me know if otherwise... so that I may adhere to my aforementioned promise directly!

Page 3 of 4 First 1234 Last