/sci/ - Science & Math

Fractional Distance: The Topology of the Real Number Line with Applications to the Riemann Hypothesis
>https://vixra.org/abs/2111.0072
>http://gg762.net/d0cs/papers/Fractional_Distance_v8-20230808.pdf
Recent analysis has uncovered a broad swath of rarely considered real numbers called real numbers in the neighborhood of infinity. Here we extend the catalog of the rudimentary analytical properties of all real numbers by defining a set of fractional distance functions on the real number line and studying their behavior. The main results of are (1) to prove with modest axioms that some real numbers are greater than any natural number, (2) to develop a technique for taking a limit at infinity via the ordinary Cauchy definition reliant on the classical epsilon-delta formalism, and (3) to demonstrate an infinite number of non-trivial zeros of the Riemann zeta function in the neighborhood of infinity. We define numbers in the neighborhood of infinity as Cartesian products of Cauchy equivalence classes of rationals. We axiomatize the arithmetic of such numbers, prove all the operations are well-defined, and then make comparisons to the similar axioms of a complete ordered field. After developing the many underlying foundations, we present a basis for a topology.

Don't say that word

>>15940417
>Will the Riemann hypothesis be solved by 2100?
Soon.

>>15940417
Why would it be solved by an particular date? Fermat's last theorem took over 300 years for someone to figure out.

>>15940465
Isn't [math]\mathbb{R}[/math] archimedean ?

>>15941877
It is.

>>15940465
Why is prop 1.8 treating an extension of infinity (however contrived) as having an order relation? Projective extensions i.e. on R are not orderable either. There are a number of rather comic liberties taken throughout and every time I glance over this I find more.