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10.- Brief and naive summary.
Posted:
Aug 31, 2007 7:07 AM
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(i) We have identified natural numbers and points of a line.
0 -> Point P_0, 1 -> Point P_1 , ..., n -> Point P_n, ...
(ii) With a fixed scale so that every real number
corresponds to a unique point on the line (real line)
we have a "name" for every natural number, for
example:
0-> 0, 1 -> 0'31, 2 -> pi, 3-> 4'2, ...
(iii) We have created on { P_n : n e N } an algebraic
structure isomorphic to the usual one ( N, +, * ). (i.e.
we have transported the arithmetic )
(iv) We have deformed the first quadrant of the xy plane,
so that we can identify prime numbers by means of
vortex points.
(v) In a natural way we can identify natural numbers and
deformed hyperbolas.
(vi) The deformed hyperbola associated to the natural
number n contains all the information about the fact of
being prime via the continuum ( i.e. behaviour of
deformed hyperbolas close to the mentioned one)
(vii) We' ll see that adequate placements of natural
numbers on the real line (in the bi dimensional sense
mentioned in (vi) ) provide relevant information about
natural numbers.
Fernando.
P.S. For previous comments see:
http://mathforum.org/kb/message.jspa?messageID=5881619&tstart=0
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