There are three facets of pi that are not finite or quantitative so we assume (hypothesize and/or hypostatize) these facets define the infinite and the qualitative (unique classes and categories).
Continuity is our first facet of infinity. It is the very nature of order. Within the finite it looks like a string of numbers and feels like time. Pi qualifies; it’s an equation that has never-ending results that are always the same and always changing.
Symmetry is the second facet of infinity. It looks like geometries and is the very nature of a relation. Within the finite it feels like space. Pi qualifies; it’s a symmetry that generates symmetries. It’s an equation that generates equations.
Harmony is the third facet of infinity. It is the very nature of dynamics; and within the finite, it is always cyclical (periodicity) and experienced as space-time moments. Pi’s numbers, geometries, and equations (Fourier transform and others) are here within an eternal dance and there’s a domain of perfection which may be experienced as a moment of perfection.
All other definitions of the infinite are put on hold. Most are personal definitions that come from personal experiences and family history. That is one’s own business, not ours. If those beliefs help you through life, that is great. Our goal here is to engage those principles and functions that give rise to mathematics, physics, and eventually all the other sciences.
Review: In this model the infinite is profoundly within the finite. It is not finite, but actively imparts qualities to the finite. For those who follow David Hilbert, please stay open. Pi’s three facets of the infinite are really real. These are not just abstractions, but realities of every circle and sphere. These three qualities condition the finite. Everything-everywhere-for all time, is in accordance with numbers, geometries, and equations; and, it all has some manifestation of these infinite qualities.
A rather different start to grasp the finite-infinite relation, our understanding of the infinite starts with pi and her most infinitesimal circles and spheres.
This document is the key part of the following homepages:
First principles: https://81018.com/principles/