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November 7th, 2017, 09:36 PM   #1
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A New Approach

$\displaystyle 0 = \left ( \begin{matrix} 0.z_1 \\ 0.z_2 \end{matrix} \right ) $

0.z1 = 0
0.z2 = 1

$\displaystyle P_1 0 = (1, 0) ~ \left ( \begin{matrix} 0.z_1 \\ 0.z_2 \end{matrix} \right ) = 1 \cdot 0.z_1 + 0 \cdot 0.z_2 = 0.z_1$

$\displaystyle P_2 0 = (0, 1) ~ \left ( \begin{matrix} 0.z_1 \\ 0.z_2 \end{matrix} \right ) = 0 \cdot 0.z_1 + 1 \cdot 0.z_2 = 0.z_2$

(0.z1) = in a binary expression of multiplication yields the product 0 : in a binary expression of division is the numerator and yields the quotient 0 : if both numbers are 0 in an expression of binary multiplication the binary product is 0

(0.z2) = in a binary expression of multiplication yields the product x : in a binary expression of division is the denominator and yields the quotient x : if both numbers are 0 in an expression of binary division the binary quotient is 0


0 = ((0z1)/1) * (1/(0z2)) = 0 * 1 = (0z1) * 1 = 0
1 = ((0z1)/1) * (1/(0z2)) = 0 * 1 = (0z2) * 1 = 1



x = x/0 = x/(-1 + 1) = ( x/-1 + x/1 ) + x = (x/0) * (1/0) = 1 * x = x



0 = x * ( 0 + 0 ) = x * (0z1) = (0z1) * x = ((0z1)/1) * (1/(0z2)) = (0z1) * x = 0

x = x * ( 0 + 0 ) = x * (0z2) = (0z2) * x = ((0z1)/1) * (1/(0z2)) = (0z2) * x = x

The distributive property (all combinations of a, b, and c as zero)

a * (b + c) = a * b + a * c

a = 1, b = 0 , c = 0
1 * ( 0 + 0 ) = 1 * 0 + 1 * 0
1 * (0 + 0) = 1 * (0.z1) = 1 * (0.z1) + 1 * (0.z2)

a = 1, b = 1 , c = 0
1 * (1 + 0 ) = 1 * 1 + 1 * (0.z1)

a = 0, b = 0 , c = 0
0 * (0 + 0) = 0 * 0 + 0 * 0

a = 1, b = 0 , c = 1
1 * (0 + 1) = 1 * (0.z1) + 1 * 1

1 = 0, b = 1, c = 0
(0.z1) * (1 + 0 ) = (0.z1) * 1 + 0 * 0
(0.z2) * (1 + 0 ) = (0.z2) * 1 + 0 * 0

Goals...
1. Relative binary multiplication by zero.
2. Defined division by zero.
3. Create varying amounts of zero.
4. Unify semantics, and physics with theoretical mathematics.
5. Offer a new approach on the continuum theory.
6. Suggest solutions for the physics regarding the unification of quantum and classical mathematics.
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November 9th, 2017, 01:25 PM   #2
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I can accept approaching zero from arbitrary paths, perhaps even curves through a very high dimensional manifold. But what does "varying amounts of zero" mean?
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November 9th, 2017, 02:00 PM   #3
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It's the same Mike Conway (if I recall correctly) with a revision of his ideas.

Goals 4, 5 and 6 seem somewhat ambitious for a system that apparently hasn't been built with any particular aspects of physics or continuum theory (hypothesis?) in mind.

I would suggest that you take a step back and consider that the lack of a multiplicative inverse is a direct result of the fact that $\{\mathbb R, +, \times\}$ is a field. That means that any system with two operations that operates members of a set as $(+,\times)$ do in the way that we are used to on numbers has the property that the additive identity has no multiplicative inverse. See here for more detail. This is a slightly circular argument, because a field is defined to be what the reals are under addition and multiplication. But it does define all the properties that contribute to the structure. In particular, it is the distributivity of multiplication over addition (but not of addition over multiplication) that breaks the symmetry.

What all this means is that, if you want to have a multiplicative inverse, you have to decide which of the properties of a group you wish to dispense with, but whatever happens you are going to break something fundamental in the number system which is likely to severely limit the utility of the system with regard to physics.
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November 9th, 2017, 03:37 PM   #4
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Originally Posted by v8archie View Post
It's the same Mike Conway (if I recall correctly) with a revision of his ideas.

Goals 4, 5 and 6 seem somewhat ambitious for a system that apparently hasn't been built with any particular aspects of physics or continuum theory (hypothesis?) in mind.

I would suggest that you take a step back and consider that the lack of a multiplicative inverse is a direct result of the fact that $\{\mathbb R, +, \times\}$ is a field. That means that any system with two operations that operates members of a set as $(+,\times)$ do in the way that we are used to on numbers has the property that the additive identity has no multiplicative inverse. See here for more detail. This is a slightly circular argument, because a field is defined to be what the reals are under addition and multiplication. But it does define all the properties that contribute to the structure. In particular, it is the distributivity of multiplication over addition (but not of addition over multiplication) that breaks the symmetry.

What all this means is that, if you want to have a multiplicative inverse, you have to decide which of the properties of a group you wish to dispense with, but whatever happens you are going to break something fundamental in the number system which is likely to severely limit the utility of the system with regard to physics.


Actually I have spent a large amount of time dealing with the field axioms.....I as of yet have not found a single axioms that "breaks". Nor have I found a change in any axioms except regarding zero.

Perhaps you would care to demonstrate where a particular field axiom breaks down. Regardless...I do NOT have to apply the idea to a field for the idea to be valid. Nor do I have to apply it to a construct for it to be valid.

Lastly your point on the last "three" goals I presented is entirely correct. It is ambitious. And entirely unfounded. Except in a subjective philosophical sense. I can discuss this...but as you point out...it is a side point...and such things haven't even really been dealt with by me...or anyone. The first three goals however are specifically addressed and "fixed" with this concept.

Again...offer a specific expression or equation that shows the failure of my "inverses".

My examples with the distributive property is enough for one to use deduction and induction for the rest of the field axioms.


Otherwise I think it proper for you to yield regarding field axioms and find another issue. Reason being is the insistence I have had from mathematicians demanding that a field remain with undefined division...because of inverses. But as I said...it does not need to be applied for the first three goals listed to be met.

I then add...that with time...the following three goals will be met....by others...because of the fundamental changes created in the construct of mathematics.

Last edited by Conway51; November 9th, 2017 at 03:46 PM.
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November 9th, 2017, 03:41 PM   #5
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Originally Posted by romsek View Post
I can accept approaching zero from arbitrary paths, perhaps even curves through a very high dimensional manifold. But what does "varying amounts of zero" mean?
This is the first serious reply from you why. I can't think you would really care what my answer to your question is.

There are things in existence that show the necessity for varying amounts of zero. Semantically....philosophically...and physically. Therefore mathematics needs a symbol to represent this.

Additionally it is a direct consequence from the inherent nature of this idea.

All numbers are composed of space and value.

The value of any given number can vary. That is what makes it a number
The space of any given number can vary. That is the declarations of units

Therefore the space of zero can vary. But not the value...as its value is undefined inherently already ( or absent).

Whether you believe this personally is a side issue. So please be nice.
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November 9th, 2017, 05:55 PM   #6
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Originally Posted by Conway51 View Post
This is the first serious reply from you why. I can't think you would really care what my answer to your question is.

There are things in existence that show the necessity for varying amounts of zero. Semantically....philosophically...and physically. Therefore mathematics needs a symbol to represent this.
name a few of these things

Quote:
All numbers are composed of space and value.
what is meant by the "space" of a number? Intervals have space. Numbers have no space. Certainly not in the Lebesgue sense.
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November 9th, 2017, 05:56 PM   #7
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Quote:
Originally Posted by v8archie View Post
It's the same Mike Conway (if I recall correctly) with a revision of his ideas.

Goals 4, 5 and 6 seem somewhat ambitious for a system that apparently hasn't been built with any particular aspects of physics or continuum theory (hypothesis?) in mind.

I would suggest that you take a step back and consider that the lack of a multiplicative inverse is a direct result of the fact that $\{\mathbb R, +, \times\}$ is a field. That means that any system with two operations that operates members of a set as $(+,\times)$ do in the way that we are used to on numbers has the property that the additive identity has no multiplicative inverse. See here for more detail. This is a slightly circular argument, because a field is defined to be what the reals are under addition and multiplication. But it does define all the properties that contribute to the structure. In particular, it is the distributivity of multiplication over addition (but not of addition over multiplication) that breaks the symmetry.

What all this means is that, if you want to have a multiplicative inverse, you have to decide which of the properties of a group you wish to dispense with, but whatever happens you are going to break something fundamental in the number system which is likely to severely limit the utility of the system with regard to physics.

V8archie


Addressing the multiplicative inverse of 0....the additive identity.

Please note....zero stays the additive identity.

Let this be our definition of multiplicative inverses...(we can change it if you like)

https://www.merriam-webster.com/dict...tive%20inverse

0's multiplicative inverse is 1..................current 0 has no defined multiplicative inverse
1's multiplicative inverse is 0.......................current 1's multiplicative inverse is 1.

all other multiplicative inverses work the same with out change

(0.z2) * 1 = 1

0.z2 multiplied by 1 yields 1

1 * (0.z2) = 1

1 multiplied by 0.z2 yields 1

the reciprocal of 0 is 1/0.z2
the reciprocal of 1 is 0.z1/1

( (0.z1)/1 ) = 0
( (1/(0.z2) ) = 1

(0.z2) * 1/(0.z2) = 1
( (0.z1)/1) * (1/(0.z2) ) = 0.z2 * 1 = 1

so when 0.z2 or 0 is multiplied by it's reciprocal (1/0.z2) the product is 1... per definition

( 1 * (0.z1)/1 ) = 1 )
( (1/(0.z2) * (0.z1)/1 ) = 1 * (0.z2) = 1

so when 1 is multiplied by its reciprocal ((0.z1)/1) the product is 1...per definition

*note it remains true that 1 is an inverse of itself as well as zero.* As it currently is an inverse of itself this is of little note at this time.
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November 9th, 2017, 06:07 PM   #8
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Originally Posted by romsek View Post
name a few of these things



what is meant by the "space" of a number? Intervals have space. Numbers have no space. Certainly not in the Lebesgue sense.

Romesk

If I hold two empty cups...one is larger than the other..one cup has more emptiness than the next cup.

There is more empty space between here and Jupiter than there is between here and the moon.

My bank account may be more empty than your empty bank account....lol...(consequences being more dire)

Zero is empty space.

Zero is NOT nothing.
Zero is space....with no value.


I have defined space and value for you in another thread. I assume you did not approve then. As you said nothing...but to troll...in this op I presented 0.z1 as value and 0.z2 as space. So then the space of 0 and the space of 1 are equivalent. This is proven on any given number line...with the equation...1 + (-1) = 0 ....
naturally the value of 0 and 1 are not equal....

Further here are some simple visual aids to help you understand what I mean by space and value...

3 = 3 values in 3 spaces
classic 3 = (1,1,1)values + ( _ , _ , _ )spaces = ( 1 , 1 , 1 ) = 3 new

2 = 2 values in 2 spaces
classic 2 = (1,1)values + ( _ , _ )spaces = ( 1 , 1 ) = 2 new

1 = 1 value in 1 space
classic 1 = (1)value + ( _ )space = ( 1 ) = 1 new

0 = 0 value in 1 space
classic 0 = (0)value + ( _ )space = ( 0 ) = 0 new
0 = (0.z1, 0.z2)

multiplication is "taking" the VALUE from one number and "putting" them in the SPACE of "another" number...then adding all values in all spaces.

Last edited by Conway51; November 9th, 2017 at 06:18 PM.
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November 9th, 2017, 06:24 PM   #9
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Quote:
Originally Posted by Conway51 View Post
Romesk

If I hold two empty cups...one is larger than the other..one cup has more emptiness than the next cup.

There is more empty space between here and Jupiter than there is between here and the moon.

My bank account may be more empty than your empty bank account....lol...(consequences being more dire)

Zero is empty space.

Zero is NOT nothing.
Zero is space....with no value.

yeah, ok. I'm done. Enjoy yourself.
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November 9th, 2017, 06:27 PM   #10
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name a few of these things



what is meant by the "space" of a number? Intervals have space. Numbers have no space. Certainly not in the Lebesgue sense.
LoL....told you....
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