Prime numbers and the continuum (9/16).
- From: fernando revilla <frej0002@xxxxxxxxxxxxxxxxxx>
- Date: Wed, 31 Oct 2007 08:18:09 EDT
9.-As a consequence we can identify primes via continuum.
Fernando.
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1.- The real line, that is a line with a fixed scale so that every real
number corresponds to a unique point on the line. The real line works
as a coding for the points of a line.
2.- Every bijective function between a half open interval and non
negative real numbers changes the coding for the points on a half-line.
3.- Peano Arithmetic is embedded into the half-open interval via bijectivity.
4.-The pairs whose coordinates are numbers of the half-open interval
constitute a "deformed plane".
5.- We transform the x y = k ( k > 0 ) hyperbolas into curves of
the deformed plane.
6.- Geometry does not identify natural number coordinate points of
the hyperbolas neither in the plane nor in the deformed plane.
7.- A natural number p is prime iff p > 1 and the only natural
coordinate points of the x y = p hyperbola are ( 1, p ) and ( p, 1 ).
8.-It is possible to obtain deformed planes in such a way that we
can identify natural coordinate points of the deformed hyperbola
of x y = n ( n natural number ). This identification is obtained in
terms of differentiability of deformed hyperbolas close to x y = n.
.
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