M.S.

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Jan 2015
30
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leskovac
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
NOTATION - natural straight line (lower case), points (capital letters or numbers (when specified point uploads metric (such as the number line)))
m (1).png
-natural gaps negation natural straight line , natural emptiness and emptiness is defined with two points
NOTATION - natural gaps (small underlined letter)
mm.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
 
Jan 2015
30
0
leskovac
Theorem - Natural straight line (natural gap) are connected in the direction of the points AB (0.1)
PROOF - straight line (gaps) b (\(\displaystyle \underline{b}\)) -defined AC (0,2)
m1.png
- straight line (gaps) c (\(\displaystyle \underline{c}\)) -defined AD (0,3)
[attachment=19586]
m2.png
infinite one way straight line (oneway infinite gaps) ∞ (\(\displaystyle \underline{\infty}\)) defined A∞ (0, ∞)
m3.png
(CM.) - straight line (not from the natural basis), there is gaps, a one-way infinite straight line the (semi-line (not from natural base)), one-way infinite gaps does not exist
 
Jan 2015
30
0
leskovac
Theorem - there is a relationship between the points 0 and all points one-way infinite straight line(one-way infinite gaps) including points 0

PROOF - relationship points 0 points 0 and the number 0
c1.png

-relationship points 0 points 1 and the number 1( \(\displaystyle \underline{1}\))
c2.png

-relationship points 0 points 2 and the number 2 (\(\displaystyle \underline{2}\))
c3.png
...

basic set of natural numbers \(\displaystyle N^o=\{0 , 1 , 2 ,3 ,4 ,5 ,...\}\)
basic set of natural numbers gaps \(\displaystyle N_p^o=\{0 , \underline{1} ,\underline{2} ,\underline{3} ,\underline{4} ,\underline{5} ,...\}\)

(CM.) - natural numbers are given as an axiom, there is no natural gaps numbers (there is this form, but do not call numbers \(\displaystyle (\{0,0\}\cup\{a,a\} a\in N)\)
 
Jan 2015
30
0
leskovac
Theorem - natural numbers and natural numbers gaps can be connected in the direction AB (0.1)

PROOF - Number 1 and number \(\displaystyle \underline {1} \)receives the combined number of \(\displaystyle 1\underline {1}\) or dup (duž , praznina )
c4.png

-Number \(\displaystyle \underline {1}\) and number 1 receives the combined number of \(\displaystyle \underline {1}1\) or dup
c5.png

-Number 1 and number \(\displaystyle \underline {2}\) receives the combined number of \(\displaystyle 1\underline {2}\) or dup
c6.png
...
- A basic set of combined natural numbers \(\displaystyle K^o=(a_n,\underline{b}_n,a_n\in{N^o},\underline{b}_n\in{N_p^o},(a_n,\underline{b}_n)>0)\)

\(\displaystyle a_1\underline{b}_1\)
\(\displaystyle \underline{b}_1a_1\)
\(\displaystyle a_1\underline{b}_1a_2\)
\(\displaystyle \underline{b}_1a_1\underline{b}_2\)
...

(CM.) - Dup do not know, not know the combined numbers (there is this form, but not numbers \(\displaystyle \{0,a\}\cup\{c,c\},\{0,0\}\cup\{a,b\},\{0,b\}\cup\{c,d\},\{0,0\}\cup\{a,b\}\cup\{c,c\},...\) )
 
Jan 2015
30
0
leskovac
Theorem - Two numbers have contact, their condition is described counts of first number

PROOF - number 3 and number 2 have a contact at point 0
\(\displaystyle 3^{\underline{0}} 2\)
cc1.png

- number 3 and number 2 have a contact at point 1
\(\displaystyle 3^{\underline{1}}2\)
cc2.png

- number 3 and number 2 have a contact at point 2
\(\displaystyle 3^{\underline{2}}2\)
cc3.png

- number 3 and number 2 have a contact at point 3
\(\displaystyle 3^{\underline{3}}2\)
cc4.png

(CM.) - Knows no contact numbers
 
Jan 2015
30
0
leskovac
Theorem - The contact number is sorted horizontally only be a natural straight line that gives a natural straight line

proof -\(\displaystyle 1\rightarrow 1\)
ccc.png
4\(\displaystyle {+_1^{\underline0}}\)2=2

4\(\displaystyle {+_1^{\underline1}}\)2=(1,1)

4\(\displaystyle {+_1^{\underline2}}\)2=2

4\(\displaystyle {+_1^{\underline3}}\)2=(3,1)

4\(\displaystyle {+_1^{\underline4}}\)2=6 or 4+2=6

\(\displaystyle +_1\) - addition rule 1

(CM.) - There are no "addition rule 1" only when the contact point number, Axiom

we were the first form of addition, the advantage of my mathematics
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question for trained mathematicians, which is a procedure to be applied in order to get (a sign?)
4 ? 2=2
4 ? 2=(1,1)
4 ? 2 =2
4 ? 2=(3,1)
4+2=6 This is known
more complex
{0,4}\(\displaystyle \cup\){6,9}\(\displaystyle \cup\){11,13} ? {0,3}\(\displaystyle \cup\){5,10} = (1,1,1,2) my solution and notation \(\displaystyle 4\underline23\underline22{+_1^{\underline0}}3 \underline25\)=(1,1,1,2)
{0,4}\(\displaystyle \cup\){6,9}\(\displaystyle \cup\){11,13} ? {0,3}\(\displaystyle \cup\){5,10} = (1,4) my solution and notation \(\displaystyle 4\underline23\underline22{+_1^{\underline1}}3 \underline25\)=(1,4)
{0,4}\(\displaystyle \cup\){6,9}\(\displaystyle \cup\){11,13} ? {0,3}\(\displaystyle \cup\){5,10} = (2,1,1,2,1) my solution and notation \(\displaystyle 4\underline23\underline22{+_1^{\underline2}}3 \underline25\)=(2,1,1,2,1)
{0,4}\(\displaystyle \cup\){6,9}\(\displaystyle \cup\){11,13} ? {0,3}\(\displaystyle \cup\){5,10} = (3,4,2) my solution and notation \(\displaystyle 4\underline23\underline22{+_1^{\underline3}}3 \underline25\) =(3,4,2)
{0,4}\(\displaystyle \cup\){6,9}\(\displaystyle \cup\){11,13} ? {0,3}\(\displaystyle \cup\){5,10} = (6,4,1) my solution and notation \(\displaystyle 4\underline23\underline22{+_1^{\underline4}}3 \underline25\)=(6,4,1)
{0,4}\(\displaystyle \cup\){6,9}\(\displaystyle \cup\){11,13} ? {0,3}\(\displaystyle \cup\){5,10} = (4,1,1,1,2) my solution and notation \(\displaystyle 4\underline23\underline22{+_1^{\underline5}}3 \underline25\)=(4,1,1,1,2)
{0,4}\(\displaystyle \cup\){6,9}\(\displaystyle \cup\){11,13} ? {0,3}\(\displaystyle \cup\){5,10} = (4,3) my solution and notation \(\displaystyle 4\underline23\underline22{+_1^{\underline6}}3 \underline25\)=(4,3)
{0,4}\(\displaystyle \cup\){6,9}\(\displaystyle \cup\){11,13} ? {0,3}\(\displaystyle \cup\){5,10} = (4,1,1,4) my solution and notation \(\displaystyle 4\underline23\underline22{+_1^{\underline7}}3 \underline25\)=(4,1,1,4)
{0,4}\(\displaystyle \cup\){6,9}\(\displaystyle \cup\){11,13} ? {0,3}\(\displaystyle \cup\){5,10} = (4,2,2,5) my solution and notation \(\displaystyle 4\underline23\underline22{+_1^{\underline8}}3 \underline25\)=(4,2,2,5)
{0,4}\(\displaystyle \cup\){6,9}\(\displaystyle \cup\){11,13} ? {0,3}\(\displaystyle \cup\){5,10} = (4,5,5) my solution and notation \(\displaystyle 4\underline23\underline22{+_1^{\underline9}}3 \underline25\)=(4,5,5)
{0,4}\(\displaystyle \cup\){6,9}\(\displaystyle \cup\){11,13} ? {0,3}\(\displaystyle \cup\){5,10} = (4,3,1,5) my solution and notation \(\displaystyle 4\underline23\underline22{+_1^{\underline{10}}}3 \underline25\)=(4,3,1,5)
{0,4}\(\displaystyle \cup\){6,9}\(\displaystyle \cup\){11,13} ? {0,3}\(\displaystyle \cup\){5,10} = (4,3,1,5) my solution and notation \(\displaystyle 4\underline23\underline22{+_1^{\underline{11}}}3 \underline25\)=(4,3,1,5)
{0,4}\(\displaystyle \cup\){6,9}\(\displaystyle \cup\){11,13} ? {0,3}\(\displaystyle \cup\){5,10} = (4,3,2,5) my solution and notation \(\displaystyle 4\underline23\underline22{+_1^{\underline{12}}}3 \underline25\)=(4,3,2,5)
{0,4}\(\displaystyle \cup\){6,9}\(\displaystyle \cup\){11,13} ? {0,3}\(\displaystyle \cup\){5,10} = (4,3,3,5) my solution and notation \(\displaystyle 4\underline23\underline22{+_1^{\underline{13}}}3 \underline25\)=(4,3,3,5)
{0,4}\(\displaystyle \cup\){6,9}\(\displaystyle \cup\){11,13} ? {0,3}\(\displaystyle \cup\){5,10} = (4,3,3,5) my solution and notation \(\displaystyle 4\underline23\underline22{+_1^{\underline{14}}}3 \underline25\)=(4,3,3,5)
 
Jan 2015
30
0
leskovac
Theorem - The contact numbers is sorted horizontally to be the only one natural straight line that gives a natural straight line , when there are two (more) results between them becomes a gap.


PROOF -\(\displaystyle 1\rightarrow1(\underline{1})\)
ccc1.png
\(\displaystyle 4{+_2^{\underline0}}2=2\)
\(\displaystyle 4{+_2^{\underline1}}2=1 \underline{2}1\)
\(\displaystyle 4{+_2^{\underline2}}2=2\)
\(\displaystyle 4{+_2^{\underline3}}2=3 \underline{1}1\)
\(\displaystyle 4{+_2^{\underline4}}2=6\)


+2 - addition rule 2


(CM.) - No "addition rule 2"
more complex
{0,4}\(\displaystyle \cup\){6,9}\(\displaystyle \cup\){11,13} ? {0,3}\(\displaystyle \cup\){5,10} = {0,1}\(\displaystyle \cup\){2,3}\(\displaystyle \cup\){6,7}\(\displaystyle \cup\){8,10} my solution and notation \(\displaystyle 4\underline23\underline22{+_{2}^{\underline0}}3 \underline25\)=111311​2
{0,4}\(\displaystyle \cup\){6,9}\(\displaystyle \cup\){11,13} ? {0,3}\(\displaystyle \cup\){5,10} = {0,1}\(\displaystyle \cup\){9,13} my solution and notation \(\displaystyle 4\underline23\underline22{+_{2}^{\underline1}}3 \underline25\)=18​4
{0,4}\(\displaystyle \cup\){6,9}\(\displaystyle \cup\){11,13} ? {0,3}\(\displaystyle \cup\){5,10} ={0,2}\(\displaystyle \cup\){4,5}\(\displaystyle \cup\){6,7}\(\displaystyle \cup\){9,11}\(\displaystyle \cup\){12,13} my solution and notation \(\displaystyle 4\underline23\underline22{+_{2}^{\underline2}}3 \underline25\)=22111221​1
...

{0,4}\(\displaystyle \cup\){6,9}\(\displaystyle \cup\){11,13} ? {0,3}\(\displaystyle \cup\){5,10} ={0,4}\(\displaystyle \cup\){6,9}\(\displaystyle \cup\){11,16} \(\displaystyle \cup\){18,23} my solution and notation \(\displaystyle 4\underline23\underline22{+_{2}^{\underline{13}}}3 \underline25\)=423252​5
 
Jan 2015
30
0
leskovac
Theorem - contact number is sorted horizontally, two natural straight line provide a natural straight line

Proof - \(\displaystyle 11\rightarrow1\)
yy.png

\(\displaystyle 2\underline{2 }2+_3^{\underline0}2\underline{2 }2=(2,2)\)

\(\displaystyle 2\underline{2 }2+_3^{\underline1}2\underline{2 }2=(1,1)\)

\(\displaystyle 2\underline{2 }2+_3^{\underline2}2\underline{2 }2=0\)

\(\displaystyle 2\underline{2 }2+_3^{\underline3}2\underline{2 }2=1\)

\(\displaystyle 2\underline{2 }2+_3^{\underline4}2\underline{2 }2=2\)

\(\displaystyle 2\underline{2 }2+_3^{\underline5}2\underline{2 }2=1\)

\(\displaystyle 2\underline{2 }2+_3^{\underline6}2\underline{2 }2=0\)

\(\displaystyle +_3\) - addition rule 3


(CM.) - No "addition rule 3"
 

topsquark

Forum Staff
Jan 2006
11,602
3,458
Wellsville, NY
This all a matter of definitions. Do you have a point to all of this?

-Dan
 
Jan 2015
30
0
leskovac
This all a matter of definitions. Do you have a point to all of this?

-Dan
I regard them as evidence, I have the author

Theorem - contact numbers, sorting is done horizontally, two natural straight lines provide a natural straight line , when there arre two (more) results between them becomes void.

Proof \(\displaystyle 11\rightarrow1(\underline1)\)
yy1.png

\(\displaystyle 2\underline{2 }2+_4^{\underline0}2\underline{2 }2=2\underline2 2\)

\(\displaystyle 2\underline{2 }2+_4^{\underline1}2\underline{2 }2=1\underline3 1\)

\(\displaystyle 2\underline{2 }2+_4^{\underline2}2\underline{2 }2=0\)

\(\displaystyle 2\underline{2 }2+_4^{\underline3}2\underline{2 }2=1\)

\(\displaystyle 2\underline{2 }2+_4^{\underline4}2\underline{2 }2=2\)

\(\displaystyle 2\underline{2 }2+_4^{\underline5}2\underline{2 }2=1\)

\(\displaystyle 2\underline{2 }2+_4^{\underline6}2\underline{2 }2=0\)

\(\displaystyle +_4\) - addition rule 4

(CM.) - No "addition rule 4"
 
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