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Posted
I will present you a math composed of only two basis (natural and realistic basis)

 

Current mathematics (CM.)

 

Natural Base

-natural straight line the main axiom, its beginning or end point and natural straight line a defined length and with two points

post-27212-0-42728400-1432192463.png

-natural gaps negation natural straight line , natural emptiness and emptiness is defined with two points

post-27212-0-92642000-1432192747.png

-basic rule merger - natural straight line and natural gaps are connected only points

-basic set - all possibilities defined theorem

(CM.) - does not know the natural straight line , point is not defined, knows no natural gap, is not defined by basic set


notation

points A, B, C, ..., metric 0, 1, 2, 3, 4, 5, 6, ...

natural straight line, points AB (0'1),  length [math]a[/math]

natural gap, points AB (0'1), gaps [math]\underline{a}[/math]


 

Posted

I don't get what your point is.

we have [math]a=\{0,4\}\cup\{6,9\}\cup\{11,13\}[/math]  , [math]b=\{0,3\}\cup\{5,10\}[/math] that should be applied a mathematical method to obtain different results of [math]c_n[/math]
 
[math]c_1=(1,1,1,2) [/math] 
[math]c_2=(1,4) [/math]
[math]c_3=(2,1,1,2,1)[/math]
[math]c_4=(3,4,2)[/math]
[math]c_5=(6,4,1)[/math]
[math]c_6=(4,1,1,1,2)[/math]
[math]c_7=(4,3)[/math]
[math]c_8=(4,1,1,1,4)[/math]
[math]c_9=(4,2,9)[/math]
[math]c_{10}=(4,5,5)[/math]
[math]c_{11}=(4,3,1,5)[/math]
[math]c_{12}=(4,3,1,5)[/math]
[math]c_{13}=(4,3,2,5)[/math]
[math]c_{14}=(4,3,3,5)[/math]

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