Relative Mathematics

[conway]

[math]0 = \left ( \begin{matrix} 0.z_1 \\ 0.z_2 \end{matrix} \right ) [/math]

​

0.z1 = 0

​0.z2 = 1

 

[math] 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[/math]

 

[math] 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[/math]

 

(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.

[pzkpfw]

...

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

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

...

Same objection as here: http://www.scienceforums.net/topic/111420-a-brand-new-approach/

 

Top line has = 0 * 1

Bottom line has = 0 * 1

Since 0 * 1 = 0 * 1, then you are implying 0 = 1.

 

It doesn't matter what else you imagine is in "0 * 1", it's what you write that matters.

 

At the very least, your notation style is broken.

[conway]

Same objection as here: http://www.scienceforums.net/topic/111420-a-brand-new-approach/

 

Top line has = 0 * 1

Bottom line has = 0 * 1

Since 0 * 1 = 0 * 1, then you are implying 0 = 1.

 

It doesn't matter what else you imagine is in "0 * 1", it's what you write that matters.

 

At the very least, your notation style is broken.

No....

 

You must convert 0 to a projection operator before you solve the binary expression

 

0 * A

 

has no product until a projection operator 0.z1 or 0.z2 has been chosen.

 

Thank your for your time.  As I told you in the other forum.  I understand you do not agree.  No reply necessary here.  Obviously

Edited November 8, 2017 by conway

[pzkpfw]

Then you are inventing non-standard notation and making gibberish.

 

If 1 = a

And 2 = a

Then both 1 and 2 equal a, so 1 and 2 are equal.

 

You have two lines of equations and both include = 0 * 1, so both lines should be equal.

 

Your notation is broken.

[conway]

Then you are inventing non-standard notation and making gibberish.

 

If 1 = a

And 2 = a

Then both 1 and 2 equal a, so 1 and 2 are equal.

 

You have two lines of equations and both include = 0 * 1, so both lines should be equal.

 

Your notation is broken.

 

I can also repeat myself...

 

 

0 * 1 = 0...if and ONLY if 0 is used as 0.z1

0 * 1 = 1...if and ONLY if 0 is used as 0.z2

[pzkpfw]

I can also repeat myself...

 

 

0 * 1 = 0...if and ONLY if 0 is used as 0.z1

0 * 1 = 1...if and ONLY if 0 is used as 0.z2

But how do you know which?

 

If you see "0 * 1" and decide to operate on it, how do you end up with 0 or 1?

 

You are sticking in context that your notation does not show.

[conway]

But how do you know which?

 

If you see "0 * 1" and decide to operate on it, how do you end up with 0 or 1?

 

You are sticking in context that your notation does not show.

It can be either

 

the expression ( A * 0 ) is RELATIVE to what "piece" of zero YOU want to use.

 

A * 0 = 0

A * 0 = A

 

Both equations exist as true...it is only that each product is relative.

We have always assumed there is only one product for this expression.  I say not.  Further I have shown you how each product has a UNIQUE solution.

[Vmedvil]

Use Standard Notation please, I don't even understand what you are talking about. 

 

Edit: 

 

Yes, Actually I do know what you are talking about but for GR that won't work it is too complex to be put in that form.

 

Einstein notation is in summations your computer would definitely stack overflow. 

 

Do you know how I know, look at the infinities this starts to cause.

 

You could do it like that in Q bits but not binary bits you start to need more than just 1 and 0 and that would even stack a quantum computer with an summation larger than its spin number on the processor. Basically, if n > n_s  n_s being the number of spin states detected by the Quantum Processor. 

Edited November 8, 2017 by Vmedvil

[conway]

Use Standard Notation please, I don't even understand what you are talking about. 

 

Edit: 

 

Yes, Actually I do know what you are talking about but for GR that won't work it is too complex to be put in that form.

 

Einstein notation is in summations your computer would definitely stack overflow. 

 

Do you know how I know, look at the infinities this starts to cause.

 

You could do it like that in Q bits but not binary bits you start to need more than just 1 and 0 and that would even stack a quantum computer with an summation larger than its spin number on the processor. Basically, if

n > n_s  n_s being the number of spin states detected by the Quantum Processor. 

 

If there was standard notation for what I am talking about I would have

 

This has absolutely nothing to so with what I am talking about.  Know how I know?  you must convert a variable to 0 before anything I have said is useful or applicable (see op and the distributive property for an example).  Then you must have a binary expression of multiplication or division ONLY.  You have neither of these elements in your equations.

 

Rewrite your notations...declare which variables you wish to discuss as zero...then we can talk.

 

 

*Also I am NOT talking about General Relativity.

 

You may note however...in the same way that the measure of "space" and "time" is relative. GR and SR

Multiplication by zero is also relative to what symbol is used as value and what symbol is used as space.

 

Relativity yes.

Edited November 8, 2017 by conway

[Vmedvil]

If there was standard notation for what I am talking about I would have

 

This has absolutely nothing to so with what I am talking about.  Know how I know?  you must convert a variable to 0 before anything I have said is useful or applicable (see op and the distributive property for an example).  Then you must have a binary expression of multiplication or division ONLY.  You have neither of these elements in your equations.

 

Rewrite your notations...declare which variables you wish to discuss as zero...then we can talk.

 

 

*Also I am NOT talking about General Relativity.

 

You may note however...in the same way that the measure of "space" and "time" is relative. GR and SR

Multiplication by zero is also relative to what symbol is used as value and what symbol is used as space.

 

Relativity yes.

 

Okay, then what about this, how would you define this in that form which is one of those in Solved Matrix, The electromagnetic Field Tensor.

 

Then here is the Euclidean metric tensor.

Then here is spherical Metric Tensor.

 

Or what about this the energy stress tensor. 

 

 

I am interested to see how you handle these real world matrices that use that form.

Edited November 9, 2017 by Vmedvil

[conway]

Okay, then what about this, how would you define this in that form which is one of those in Solved Matrix, The electromagnetic Field Tensor.

 

Then here is the Euclidean metric tensor.

Then here is spherical Metric Tensor.

 

Or what about this the energy stress tensor. 

 

 

I am interested to see how you handle these real world matrices that use that form.

All that information was given to you in the original post.

 

Only in a binary expression of multiplication or division involving zero is this applicable.

 

Every example given by you involving zero...involves zero in a matrix and so forth....therefore not applicable.

 

In a given case where zero requires a certain projection operator...fine...I have put no bounds on when and where a projection operator can of can not be used.

 

Therefore any case presented by "you" or "physics" still have the current product of multiplication by zero available.

 

Please note there are cases in physics that arrive at division by zero...

It is in these cases that this is applicable....but work has yet to be done.. in that regard..naturally.

Edited November 9, 2017 by conway

[Vmedvil]

All that information was given to you in the original post.

 

Only in a binary expression of multiplication or division involving zero is this applicable.

 

Every example given by you involving zero...involves zero in a matrix and so forth....therefore not applicable.

 

In a given case where zero requires a certain projection operator...fine...I have put no bounds on when and where a projection operator can of can not be used.

 

Therefore any case presented by "you" or "physics" still have the current product of multiplication by zero available.

 

Please note there are cases in physics that arrive at division by zero...

It is in these cases that this is applicable....but work has yet to be done.. in that regard..naturally.

 

So, what then this is used to remove "Divide by zero" errors in computers?

Edited November 9, 2017 by Vmedvil

[conway]

This then makes it unnecessary to have to remove division by zero errors.  As it makes division by zero possible in a typical field.  (much contention here naturally).  

 

As far as I am aware there are cases in physic where division by zero is the binary operation used.  Such as the merging of classical and quantum mechanics regarding black wholes.  And the merging of quantum mathematics and classical mathematics in general. You are probably already aware of this...if not I can post a few links.  However this is still at the point, where it must be accepted and "finalized" by mathematicians...before it is really ready for physics.

 

You might notice the six goals that were posted in the op.  The last one being the application to physics and quantum mechanics.  To many questions to pin down really before that is given serious attention.  But....as I have said...physics aside there are other benefits.

 

Essentially this is nothing more than a system of multiplication and division that makes operations by zero well defined.  And it is constructed in such a way as to be RELATIVE. That is....Take the "theory of relativity"....then apply it to mathematics......where space and time are "measured" relative...so to are the products of multiplication and division...

 

Here are some simple visual aids.....

 

 

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.

 

​*note* Therefore 0 has space.

 

This extends with division but inverse.

 

​Lastly...it is possible to apply this to a given matrix.  I gave projection operators.  But to apply them to the matrix's given by you would be an extensive job.  Take only the first  matrix given.  Chose your binary operations.....0...must be included....then chose a projection operator from the op for zero...then apply to the binary operation (from the matrix) you chose....Two sums are yielded....one for each different projection operator that can be chosen for zero.  

 

Thank you for your time.

Edited November 9, 2017 by conway