Exploring Unconventional Addition: Can Mathematics Embrace New Foundations?

[biljanica]

Can mathematics rest on new foundations? See the attachment.

a little explanation about the form of addition

adding or joining , as performed

R a+b=c same as now, combined numbers 222+33=2253, when they are the same along (gap) they are joined, here 2 and 3, we get 5

R²
here there is an operation function (the same applies to other Rⁿ) , 1(R₂) 3+₁4=(3,4₂) , 2(R,R₂) 3₊₂4={7 ,(3,4₂)} , 3(R-R₂) 3+₃4= (7, 4₂₎},4(R,R₂,R-R₂) , 3+₄ 4={7,(3,4₂) , (7.4₂)}
(2,3₂)+(3.3₂)=(5 .6₂)

R³ 5(R,R₂ , R₃) , 3+₅4={7 , (3 ,4₂ ), (3 , 0 , 4₃)} , 6(R-R₂, R₃) , 3+₆4={( 7 , 4₂) , ( 3 , 0 , 4₃} , 7(R, R₂-R₃) , ...so on

 

[jedishrfu]

Welcome to PF!

What are you trying to do?

Is this for a class on group theory?

I don't see a practical application of your new definition of addition.

 

[fresh_42]

Can mathematics rest on new foundations?

Can? Why not. Will? Definitely not.

I have no idea what you are talking about.

 

[biljanica]

you have two points, how would you describe them with numbers
1. there is no line between the points
2. there is a line between the points
3. there is a line between the points, parts of the line are erased
practical application of my mathematics

axion
there is length 0-1 there is gap 0 - 1
ten times smaller than 0 - 0.1 ( 0-0. 1 )
a hundred times smaller than 0- 0.01 ( 0- 0.00 1 )
...

With me, rights are plans, evidence not axion.

there are gap and combined numbers and linear complex

This is just the beginning, there is much more.

Be sure to check out the attachment.

 

[fresh_42]

you have two points, how would you describe them with numbers
1. there is no line between the points
2. there is a line between the points
3. there is a line between the points, parts of the line are erased
practical application of my mathematics

axion
there is length 0-1 there is gap 0 - 1
ten times smaller than 0 - 0.1 ( 0-0. 1 )
a hundred times smaller than 0- 0.01 ( 0- 0.00 1 )
...

With me, rights are plans, evidence not axion.

there are gap and combined numbers

This simply does not make any sense and contains nothing that couldn't be dealt with by ordinary math.

This is just the beginning, there is much more.

I don't hope so.

Be sure to check out the attachment.

Definitely not.

 

[bob012345]

It’s hard to follow what you are doing. Have you gotten feedback from math people you know in person?

 

[phinds]

You're going to have to be a lot more clear about what you are doing / trying to do since what you have so far sounds like utter nonsense in practical terms.

 

[berkeman]

Thread is done. @biljanica -- PF is not the place for you to try to develop your new ideas.

 

[Mark44]

Be sure to check out the attachment.

I did, and it makes no sense at all.
Right at the start you have a couple axioms for "basics length" and "basics gaps." The figures next to them make no sense.
Right after the axioms you have a theorem whose "proof" also makes no sense.
Later, in the section titled "set of points" you have this: $B_d = \{0\infty1\infty2\infty3\infty4\infty5.. \}$ with your own definition of the symbol $\infty$, which is completely at odds with the usual definition of this symbol. Your definition appears to define the symbol $\infty$ as all of the numbers between 0 and 1.

Nothing I've seen in your paper makes any sense to me.