So, you're trying to reinvent limits? Nice, but you're some centuries late in that.
Yes, the singularity of 1/x can be "removed", even on the complex plane if you add an infinity point to make it a sphere, it becomes a simple reflection
Now Riemann's function is a wee bit more difficult
Yes, the singularity of 1/x can be "removed", even on the complex plane if you add an infinity point to make it a sphere, it becomes a simple reflection
Now Riemann's function is a wee bit more difficult
Code:
( ∀𝑥 𝑥 ∈ (−0⁺, 0⁺) ) ⇒ ( −0 ± 𝑥 = {−𝑥, 𝑥} ) ∧ ( 0 ± 𝑥 = {0⁻ + 𝑥, 0⁺ − 𝑥} )
It is not an infinity point (coric), for such a point would not accomodate conventional mathematics hyperreal numbers. Instead, it is an originone that has been missed sorely.
Earths set of all real numbers is, essentially, a Möbius strip fashioned from a line where one surface extends from 0⁻ to −0⁻, the other from −0⁺ to 0⁺, and all edges are retained.