**Abstract**: A mathematical convenience truncates real analysis and discussion of the transformation nexus between the finite and infinite. A short-term trick became a long-term solution to ignore the most fundamental transition that defines our universe. The first challenge is to define the infinite in a way that respects its beingness yet opens possibilities for new analyses. Although initiated back in 1971, that three-part description — continuity (order), symmetry (relations) and harmony (dynamics) — is re-engaged to test to see if all words can satisfactorily be used to describe an aspect or face of the infinite.

This body of this document will finally be written as a result of these studies of the finite-infinite relation and renormalization outlined here.

**Planckspheres**.** **Within this model the Planck spheres are being generated one at a time, just as imaged above. That is the sole action of the first notation and the piling on as imaged with its sequences happens as part of the notational activity over time.

**References**:

- https://en.wikipedia.org/wiki/Renormalization
- https://en.wikipedia.org/wiki/Renormalization_group
- https://en.wikipedia.org/wiki/Scale_invariance
- https://en.wikipedia.org/wiki/Transformation_(function)
- https://en.wikipedia.org/wiki/Matrix_theory_(physics)

- https://81018.com/2017/11/04/infinitude/
- https://81018.com/2018/03/14/hawking-pi/
- https://81018.com/pi-day/
- https://81018.com/pi2/
- https://81018.com/view/

Schrödinger_equation:

https://en.wikipedia.org/wiki/Schrödinger_equation

Not to be confused with Schröder’s’equation

https://en.wikipedia.org/wiki/Schröder%27s_equation