Mirror-Pair-Function, A Number Theoretical Exploration

A finite, exact approach to digit symmetry and self-similarity with implications for the foundations of mathematics. Every finite natural number other then one digit numbers have a Mirror-Pair. Thus any finite natural two digit number has a Mirror-Pair. If the pair is plugged in into the function 𝑀b(𝑥) it becomes it’s Mirror-Pair, and if it’s Mirror-Pair is plugged into the function 𝑀b(𝑥) it arrives back at itself again. Zero and infinity are not numerical Mirror- Pairs of each other and are excluded, because they are conceptual Mirror-Pairs (more about that in the in-depth appendix).

- In diffrent bases the spread in x and y direction shifts relative to the respective base. In base 10 there is always a Mirror-Pair in transitions from n+1 in 10𝑛+1, that will say from 10(10^1) to 100 (10^2). From 100(10^2) to 1000 (10^3). From 1000(10^3) to 10000(10^4). And so on and so forth.

-The Mirror-Pair-Function 𝑀b(𝑥) shows how human perceive numbers and which symmetry arises in the way we do that.

-When the Mirror-Pair-Function 𝑀b(𝑥) is plotte don the log-log-scale self-similarity reappears at any order of magnitude, hence self-similarity and bound-fractals can be generated and explained finitistically.

-This relates naturally to the Lychrel-numbers