# M.S.

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#### point1967

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)))

-natural gaps negation natural straight line , natural emptiness and emptiness is defined with two points
NOTATION - natural gaps (small underlined letter)

-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

#### point1967

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)

- straight line (gaps) c ($$\displaystyle \underline{c}$$) -defined AD (0,3)
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infinite one way straight line (oneway infinite gaps) ∞ ($$\displaystyle \underline{\infty}$$) defined A∞ (0, ∞)

(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

#### point1967

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

-relationship points 0 points 1 and the number 1( $$\displaystyle \underline{1}$$)

-relationship points 0 points 2 and the number 2 ($$\displaystyle \underline{2}$$)

...

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 $$\displaystyle (\{0,0\}\cup\{a,a\} a\in N)$$

#### point1967

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 )

-Number $$\displaystyle \underline {1}$$ and number 1 receives the combined number of $$\displaystyle \underline {1}1$$ or dup

-Number 1 and number $$\displaystyle \underline {2}$$ receives the combined number of $$\displaystyle 1\underline {2}$$ or dup

...
- 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 $$\displaystyle \{0,a\}\cup\{c,c\},\{0,0\}\cup\{a,b\},\{0,b\}\cup\{c,d\},\{0,0\}\cup\{a,b\}\cup\{c,c\},...$$ )

#### point1967

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
$$\displaystyle 3^{\underline{0}} 2$$

- number 3 and number 2 have a contact at point 1
$$\displaystyle 3^{\underline{1}}2$$

- number 3 and number 2 have a contact at point 2
$$\displaystyle 3^{\underline{2}}2$$

- number 3 and number 2 have a contact at point 3
$$\displaystyle 3^{\underline{3}}2$$

(CM.) - Knows no contact numbers

#### point1967

Theorem - The contact number is sorted horizontally only be a natural straight line that gives a natural straight line

proof -$$\displaystyle 1\rightarrow 1$$

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)

#### point1967

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 -$$\displaystyle 1\rightarrow1(\underline{1})$$

$$\displaystyle 4{+_2^{\underline0}}2=2$$
$$\displaystyle 4{+_2^{\underline1}}2=1 \underline{2}1$$
$$\displaystyle 4{+_2^{\underline2}}2=2$$
$$\displaystyle 4{+_2^{\underline3}}2=3 \underline{1}1$$
$$\displaystyle 4{+_2^{\underline4}}2=6$$

(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

#### point1967

Theorem - contact number is sorted horizontally, two natural straight line provide a natural straight line

Proof - $$\displaystyle 11\rightarrow1$$

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

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

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

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

$$\displaystyle 2\underline{2 }2+_3^{\underline4}2\underline{2 }2=2$$

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

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

$$\displaystyle +_3$$ - addition rule 3

(CM.) - No "addition rule 3"

#### topsquark

Forum Staff
This all a matter of definitions. Do you have a point to all of this?

-Dan

#### point1967

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 $$\displaystyle 11\rightarrow1(\underline1)$$

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

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

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

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

$$\displaystyle 2\underline{2 }2+_4^{\underline4}2\underline{2 }2=2$$

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

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

$$\displaystyle +_4$$ - addition rule 4

(CM.) - No "addition rule 4"

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