Mathematics - a new basis

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I switched on your recommendation-​-Dan
See a picture that represents the relations of the two triangles


what is a "?"
3?3=3
3?3=4
3?3=5
3?3=6
3?3=7
3?3=8
3?3=9
3?3=10
3?3=12
 
Jan 2012
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When you look at the solution below will not be clear
1. 3 + [0] 3 = 3
2. 3 + [1] 3 = 4
3. 3 + [2] 3 = 5
4. 3 + [3] 3 = 6 or 3 +3 = 6
5.33Rd1 (6) d2 (7) +3 = 7
6.33Rd1 (6) d2 (8) +3 = 8
7.33Rd1 (6) d2 (9) +3 = 9
8.33Rd1 (6) d2 (10) +3 = 10
9.33Rd1 (6) d2 (12) +3 = 12
(1,2,3,4) - There are many forms of addition in the set N
(5,6,7,8,9) - numbers that are dynamic, where it is possible to add this
 
Jan 2012
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1 Mathematics Space
We'll tell mathematical space with two initial geometric object that can not
prove.
1.Natural geometric object - natural straight line .
2.Real geometric objects - real straight lines .
1.1 Natural along
In the picture there is a natural geometric object straight line (AB), it has a beginning (A)
and end (B) - this property natural long'll call point.

w1.png

1.2 The basic rule
Two (more) natural straight line are connected only with points.
 
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2 Natural Mathematics
2.1 straight line , semi-line "1"
"1"-from any previous evidence (axioms), a new proof
Theorem-Two (more) natural straight line merge points in the direction of the first AB
natural straight line .

EVIDENCE - natural straight lines (AB, BC) are connected - we get straight line AC.

w2.png

Natural straight lines (AB, BC, CD) are connected - we get straight line AD.

w3.png

Natural straight lines (AB, BC, CD, DE) are connected - we get straight line AE.

w4.png
...

Natural straight lines (AB, BC, CD, DE, ...) are connected - getting semi-line.

w5.png
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Comparability of the two mathematics ( down what is given of the current mathematics)
straight line - EVIDENCE ( line - Axiom)
semi-line - EVIDENCE (line -Axiom )
 

HallsofIvy

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I am confused as to what is "new" about this. It looks to me like basic Euclidean geometry but with vague and poorly stated definitions instead of the standard definitions.
 
Jan 2012
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I am confused as to what is "new" about this. It looks to me like basic Euclidean geometry but with vague and poorly stated definitions instead of the standard definitions.
Geometry but not the basis of the whole of mathematics, unlike Euclid I only have two axioms (natural straight line - with which you are familiar)
This is a different approach than the current math, the fewer rules (axiom)
Because these rules (axioms) to limit the the phenomena that exist in real life can be mathematically explained (I gave an example of the early post)
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2.2 Numeral semi-line, numeric point "2.1"
Theorem-character mark points on the one-way infinite
long (A, B, C, ...), replace the labels {(0), (0.1), ..., (0,1,2,3,4,5,6,7,8,9 ), ...}
which are set circular and positionally.
w6.png
Proof - is obtained by numerical along which the numerical point of {(0,00,000,
0000, ...), (​​0,1,10,11,100,101, ...), ..., (0,1,2,3,4,5,6,7,8,9,10,11, 12, ...), ...}.
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2.3 Natural numbers "2.2"
Theorem - There is a relationship (length) between Point in numeric (0) and
all points Numeral semi-line.

Proof - Value (length) numeric point (0) and numerical point (0)
the number 0

w7.png

Ratio (length) numeric point (0) and the numerical point of (1) the number o1

w8.png

Ratio (required) numeric point (0) and numeric item (2) is the number 2

w9.png

Ratio (length) numeric point (0) and the numerical point of (3) is the number 3

w10.png

Ratio (length) numeric point (0) and the numerical point of (4) is the number 4

w11.png
...
Set - all the possibilities given theorem.
The set of natural numbers N = {0,1,2,3,4,5,6,7,8,9,10,11,12, ...}.
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Comparability of the two mathematics ( down what is given of the current mathematics)
numeral semi-line - axiom
numerical point - axiom
set - axiom
natural numbers -axion
 
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2.4 Mobile Number "2.2,2.3"
Theorem-Natural numbers can be specified and other numerical
point other than the point numeric 0th
Proof - Value (length) numeric point (0) and numeric point (2)
the number 2
w12.png
Ratio (length) numeric point (1) and the numerical point of (3) is the number 2
w13.png
Ratio (length) numerical point (2) and the numerical point of (4) is the number 2
w14.png
...
A set of mobile numbers Nn = {[n]N}
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2.5 Gap numbers "2.2,2.3,2.4"
Theorem - Natural number and mobile number of no contact,
(natural number and mobile number no contact) and have no contact mobile number, ..., in numeric longer.

EVIDENCE - natural number 2 and mobile number 2 no contact, you get the number of gaps 2/.1/2.
w15.png
natural number 2 and mobile number 2 no contact, you get the number of gaps 2/.2/2.
w16.png
natural number 2 and mobile number 2 no contact, you get the number of gaps 2/.3/2.
w17.png
...
(natural number 2 and mobile number 2 no contact) and mobile number 1 no contact , you get the number of gaps
2/.1/2/.1/1
w18.png
...
Set gap number GN={a|/.bn/cn|(a,bn,cn)\(\displaystyle \in\)\(\displaystyle N\),bn>0}
a/.b1/c1
a/.b1/c1/.b2/c2
a/.b1/c1/.b2/c2/.b3/c3
a/.b1/c1/.b2/c2/.b3/c3/.b4/c4
...
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Comparability of the two mathematics ( down what is given of the current mathematics)
mobile number - no
gap number - no
 
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2.6. Mobile gap number "2.2,2.5"
Theorem-Gap numbers can be entered and the second numerical
point other than the point numeric 0th

EVIDENCE-ratio (length) numeric point (0) and the numerical point of (4) is
2/.1/1 number of gap.

w19.png

ratio (length) numeric point (1) and the numerical point of (5) is
2/.1/1 number of gap.

w20.png

ratio (length) numeric point (2) and the numerical point of (6) is
2/.1/1 number of gap.
w21.png
...
A set of mobile numbers gap GNn={[n]GN}
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2.7. Points the number of "2.2,2.3,2.5"
Theorem - Number (N,GN) has extended the numeric point, they
can write the opposite.

EVIDENCE - Number 5 has a point: [0], [1], [2], [3], [4], [5]. Opposite may
write: [.0], [.1], [.2], [.3], [.4], [.5].

w22.png

Gaps has a number 2/.3/1 points: [0], [1], [2], [3], [4], [5], [6]. They can be
otherwise write: [.0], [.1], [.2], [.3], [.4], [.5), [.6].
w23.png
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Comparability of the two mathematics ( down what is given of the current mathematics)
mobile gap number - no
point number - no
 
Apr 2012
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Erewhon
2.6. Mobile gap number "2.2,2.5"
Theorem-Gap numbers can be entered and the second numerical
point other than the point numeric 0th

EVIDENCE-ratio (length) numeric point (0) and the numerical point of (4) is
2/.1/1 number of gap.

View attachment 27023

ratio (length) numeric point (1) and the numerical point of (5) is
2/.1/1 number of gap.

View attachment 27024

ratio (length) numeric point (2) and the numerical point of (6) is
2/.1/1 number of gap.
View attachment 27025
...
A set of mobile numbers gap GNn={[n]GN}
-------------
2.7. Points the number of "2.2,2.3,2.5"
Theorem - Number (N,GN) has extended the numeric point, they
can write the opposite.

EVIDENCE - Number 5 has a point: [0], [1], [2], [3], [4], [5]. Opposite may
write: [.0], [.1], [.2], [.3], [.4], [.5].

View attachment 27026

Gaps has a number 2/.3/1 points: [0], [1], [2], [3], [4], [5], [6]. They can be
otherwise write: [.0], [.1], [.2], [.3], [.4], [.5), [.6].
View attachment 27027
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Comparability of the two mathematics ( down what is given of the current mathematics)
mobile gap number - no
point number - no
You a crank and I claim my $64,000 reward.

.
 
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Jan 2012
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You a crank and I claim my $64,000 reward.

.
is this a joke, or actually give the money
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2.8. The opposite number "2.2,2.3,2.5,2.7"
Theorem - Numbers (N, GN) that have the same number of points
number, length becomes gap and rotation.
EVIDENCE - 4 \(\displaystyle \fbox{s}\) 0/.4/0 , 4s. = {4, 0/.4/0 } or 0/.4/0s.= {0/.4/0,4}.

w24.png

1/.1/3 \(\displaystyle \fbox{s}\) 0/.1/1/.3/0 , 1/.1/3s. = {1/.1/3, 0/.1/1/.3/0} or
0/.1/1/.3/0s. ={ 0/.1/1/.3/0, 1/.1/3}

w25.png

The general form of a \(\displaystyle \fbox{s}\) b. as.= {a, b} or bs. = {b, a}.

A set of numbers opposing S. = {(a, b) \(\displaystyle \in\)(N, GN)}, S.n = {(a, b)\(\displaystyle \in\) (Nn, GNn)}
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2.9 N comparability numbers "2.3"
Theorem - Two (more) numbers are comparable to
know who is higher (equal or smaller), which is the point of [.0] away
from the numerical point of 0th

EVIDENCE - Two numbers: 5> 3 (item number 5 [5] is far from the point
3 of [3] 5 is a number of third 4 = 4 (item number 4 [4] and the number of points
4 [4] are equidistant) 4 is equal to 4 .2 <6 (item number 6 [6] is
from the point of 2 [2] 2 less than sixth ). .(={>, =, <}.

The general form of a). .(b

Three numbers: a). .(b). .(c (general form, open, closed form (the
figure)).

w26.png

...
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Comparability of the two mathematics ( down what is given of the current mathematics)
opposite number -no
N comparability numbers - axiom
 
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