Starting from 2 to remove division by zero from the equation.

[abstract]

The number 2

What if the number 2 is the origin of whole numbers? (Instead of 0)

The criteria for a whole number would contain that a whole number would primarily need to be wholly divisble by 2.

does 2/2 = 2
as there are 2 combinations of the halves of 2
I think this can be explained by the 2 possible combinations of:
(2/4+2/4)+(2/4+2/4)=2
(a+b)+(a+a)/(b+b)+(b+a)
As I believe it to be 1/2 is not a number it is mearly a concept of quantity.
let me know?

so in theory, 2 can be divided into 2 1/2 parts giving a "conceptual" quantity of half of the original whole, the number 4 on the other hand can be divided into 2 whole parts of 2, a whole quantity.

why bother?
well 0/0=huh? and 1/0 or 0/1 = huh? so would starting with a whole quantity containing a pair of whole halves not make a cleaner starting point in modern mathmatics?
I asked about zero here once before.To date I believe there's no clear concensus.

Would this make odd numbers mearly place holders like factions or decimals, would pi have no end as it would be an (i think the term is "irrational") non 2 based number?

Taking it way out there, think of 2 as a quantity of "what is" and "what was" two parts of "what will be"
half of "what was" has to be its own whole as does "what was"
so as 1/2 is a 1/2 more than 0,or 1/2 of 1(which is accually still one quantity) both being concepts not whole quantities,
Would a system that starts at 2 not be more logical since 1/2 of 2 would be 1 whole quantity?

I dunno, but as nature goes would it not be more likely we have out-grown the need for the conceptual nothing found in 0 and the self preservation found in 1.

just throwing it out there.

i'm no mathmatian as your no doubt aware, just an artist with an imagination that is facinated with the "what if".

What was clear to me has probly not been conveyed here but, with work and direction, together we can learn.

Thanks for reading my ravings.




ps.
and yes this probly belongs in a philosophy post or something.

 

[abstract]

after reading this thread:
https://www.physicsforums.com/showthread.php?s=&threadid=11688

sorry as facinating as it is, I only understood a fraction of it.
I hate to bump my own post but,

using the notation or principles from that post can I use
the following to explain a bit more?

{}=2x
{.}=2x
{-}=2x


[?]

 

[HallsofIvy]

Wouldn't arithmetic be a heck of a lot harder without an additive identity?

 

[Organic]

Hi Abstract,

First, thank you for looking at my thread.

Professional mathematicians don't like philosophical definitions when they make Math, because in math everything must be well defined before we can use it.

Because I am not a Professional mathematician, I allow myself to think on Math in a non-traditional way.

Sometimes a new point of view on "well defined terms" can lead you to find a new way to understand the fundamentals of some system (and in this case, the fundamentals of Mathematics language).

For example in Math Langauge there is no definition to the concept of a Number.

If you ask a Professional mathematician: "What is a Number?" instead of an answer you get the question: "What kind of a number, Natural , Integer, Rational, Irrational, Algebraic, Complex ?"

There is no general definition in Standard Math that answer to the question:
"What is a number?"

If we want to find a general definition to this question, we have to look on Math as a private case of a more general concept.

I have found that 'information' is the concept, where Math language is a private case of it.

Also I have found that a good approach to explode new ideas, is to look for the simplest way that you can get.

So, when we think about information, then in the first stage we have no information at all.

The concept of a 'set' (a collection of objects) is one of the simplest concepts used by Math, to construct (or define) its own ideas.

When we combine the idea of no information with the set's concept, we get {}, which is a set with no content, known as the empty-set.

The Axiom of the empty-set is:

If A is a set such that for any x, x not in A, then A={}(=Empty set).

But from an informational point of view we can see that there is here an hidden assumption, which is: x cannot be nothing, otherwise A is not an empty-set by the above axiom.

In other words A property depends on the property of x, that can be at least nothing (no information) XOR something (some information).

If we want to save the symmetry of our mathematical system (symmetry is a very powerful concept that cannot be ignored, when we define some mathematical terms), then if we have an empty-set (notated as {}), then we have (from symmetrical point of view) a full-set (notated as {__}) as its opposite concept.

Another powerful concept in Math is the limit concept, which says that some mathematical system approaching but cannot be closer to some unreachable state.

As we know by the informational point of view, our unreachable limits are {}(=empty-set), {__}(=full-set), or in more formal way:
the open interval of ({}, {__}).

So, {} XOR {__} are "out of the scope" of any useful information system, therefore if we want to define some useful mathematical tools (like numbers for instance) we can define them only between these limits.

To know more about this approach please read:

http://www.geocities.com/complementarytheory/Everything.pdf

http://www.geocities.com/complementarytheory/ASPIRATING.pdf

About 2x please read:

http://www.geocities.com/complementarytheory/LIM.pdf


Yours,

Organic

 

[Hurkyl]

Abstract, you're right, this probably belongs in one of the philosophy forums; if this keeps heading in the same direction I'll move it over there.


From a practical point of view, I don't see how what you are doing is anything but labelling things; how would any of your suggestions actually change how anything is done? And if there is a change, does this change have any practical benefits?


Also, I'm not sure what you are trying to suggest by calling fractions and decimals "placeholders".


Anyways, it looks to me like you're, for the most part, just being poetic. Aesthetics are nice, it's fun to play around with math; you should try actually building the system you describe rather than wondering about it. However, I will advise against believing (until you are faced with concrete evidence) that trying to eliminate 0 and 1 is a practical pursuit.

sorry as facinating as it is, I only understood a fraction of it.
I hate to bump my own post but,

using the notation or principles from that post can I use
the following to explain a bit more?

For the record, at most one person understands the post you linked. Using Organic's notation certainly isn't the best way to try and make yourself better understood.

 

[Organic]

Dear Hurkyl,

Can we ignore this?

The Axiom of the empty-set is:

If A is a set such that for any x, x not in A, then A={}(=Empty set).

But from an informational point of view we can see that there is here an hidden assumption, which is: x cannot be nothing, otherwise A is not an empty-set by the above axiom.

In other words A property depends on the property of x, that can be at least nothing (no information) XOR something (some information).

Also can we ignore the symmetric point of view of ({},{__})
that clearly shown here? :

http://www.geocities.com/complementarytheory/Everything.pdf

http://www.geocities.com/complementarytheory/ASPIRATING.pdf

You are already a participator in it.



------------------------------------------------------------------------------

Is this meaningless to you? :

http://www.geocities.com/complementarytheory/CompLogic.pdf

http://www.geocities.com/complementarytheory/4BPM.pdf

By Complementary Logic multiplication is noncommutative, but I think that another interesting result is the fact that multiplication and addition are complementary, and as much as I know this point of view has a very deep influence on the question: "What is a Number?"

Answer: A Number is anything that exist in ({},{__})

Or in more formal definition:

({},{_}):={x|{} <-- x(={.}) AND x(={._.})--> {_}}

Where -->(or <--) is ASPIRATING(= approaching, but cannot become closer to) as we clearly can see here:

http://www.geocities.com/complementarytheory/LIM.pdf


If x=4 then number 4 example:

Number 4 is a fading transition between multiplication 1*4 and
addition ((((+1)+1)+1)+1) ,and vice versa.

This fading can be represented as:

(1*4)              ={1,1,1,1} <------------- Maximum symmetry-degree, 
((1*2)+1*2)        ={{1,1},1,1}              Minimum information's clarity-degree
(((+1)+1)+1*2)     ={{{1},1},1,1}            (no uniqueness)
((1*2)+(1*2))      ={{1,1},{1,1}}
(((+1)+1)+(1*2))   ={{{1},1},{1,1}}
(((+1)+1)+((+1)+1))={{{1},1},{{1},1}}
((1*3)+1)          ={{1,1,1},1}
(((1*2)+1)+1)      ={{{1,1},1},1}
((((+1)+1)+1)+1)   ={{{{1},1},1},1} <------ Minimum symmetry-degree,
                                            Maximum information's clarity-degree 
                                            (uniqueness)
============>>>

                Uncertainty
  <-Redundancy->^
    3  3  3  3  |          3  3             3  3
    2  2  2  2  |          2  2             2  2
    1  1  1  1  |    1  1  1  1             1  1       1  1  1  1
   {0, 0, 0, 0} V   {0, 0, 0, 0}     {0, 1, 0, 0}     {0, 0, 0, 0}
    .  .  .  .       .  .  .  .       .  .  .  .       .  .  .  .
    |  |  |  |       |  |  |  |       |  |  |  |       |  |  |  |
    |  |  |  |       |__|_ |  |       |__|  |  |       |__|_ |__|_
    |  |  |  |       |     |  |       |     |  |       |     |
    |  |  |  |       |     |  |       |     |  |       |     |
    |  |  |  |       |     |  |       |     |  |       |     |
    |__|__|__|_      |_____|__|_      |_____|__|_      |_____|____
    |                |                |                |
    (1*4)            ((1*2)+1*2)      (((+1)+1)+1*2)   ((1*2)+(1*2))
 
 [b]4 =[/b]                                  2  2  2
          1  1                        1  1  1          1  1
   {0, 1, 0, 0}     {0, 1, 0, 1}     {0, 0, 0, 3}     {0, 0, 2, 3}
    .  .  .  .       .  .  .  .       .  .  .  .       .  .  .  .
    |  |  |  |       |  |  |  |       |  |  |  |       |  |  |  |
    |__|  |__|_      |__|  |__|       |  |  |  |       |__|_ |  |
    |     |          |     |          |  |  |  |       |     |  |
    |     |          |     |          |__|__|_ |       |_____|  |
    |     |          |     |          |        |       |        |
    |_____|____      |_____|____      |________|       |________|
    |                |                |                |
(((+1)+1)+(1*2)) (((+1)+1)+((+1)+1))  ((1*3)+1)        (((1*2)+1)+1)

   {0, 1, 2, 3}
    .  .  .  .
    |  |  |  |
    |__|  |  |
    |     |  |
    |_____|  |
    |        |
    |________|
    |    
    ((((+1)+1)+1)+1)

Multiplication can be operated only among objects with structural identity, where addition can be operated among identical and non-identical (by structure) objects.

Also multiplication is noncommutative, for example:

2*3 = ( (1,1),(1,1),(1,1) ) , ( ((1),1),((1),1),((1),1) )

3*2 = ( (1,1,1),(1,1,1) ) , ( ((1,1),1),((1,1),1) ) , ( (((1),1),1),(((1),1),1) )

Also you wrote:

And if there is a change, does this change have any practical benefits?

Between us, do you really don't see the practical benefits?



Yours,

Organic