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.
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
Ratio (length) numeric point (0) and the numerical point of (1) the number o1
Ratio (required) numeric point (0) and numeric item (2) is the number 2
Ratio (length) numeric point (0) and the numerical point of (3) is the number 3
Ratio (length) numeric point (0) and the numerical point of (4) is the number 4
...
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