An introduction to infinity and the infinitesimals

Can we further define these two?

Throughout history, the finite-infinite debate has been fraught with emotion between those who “believe” and those who do not.

Those debates are ignored here.

We attempt to start with a clean slate — tabula rasa — by starting with most simple concepts that defy a finite label. Then, we look at some of the most advanced concepts of the infinite, the current work within renormalization and regularization whereby infinities are carefully analyzed so to control their mathematical and physical influence.

What are our most advanced concepts about infinity and infinitesimals? The highly-technical descriptions of infinity and the infinitesimals by our most erudite scholars have yielded concepts with highly-specialized language. Some of that work will be engaged, but always with a goal of discovering new relations that could be used to influence general perceptions away from Newton’s absolutes.

To start simply and modestly, the qualities of pi were analyzed.

Then, turning to the classic studies of the electron defined as a point particle with a point charge and no spatial extent. The radius formula is:


Within our base-2 chart, this “point” particle falls within Notation 60. There are 60 doublings of the Planck scale numbers prior to reaching the size of a “point” particle. Denying this infinitesimal range seems a bit too sure that particles and waves are our fundamental building blocks with which to construct our universe. A key concept of this website is that the most simple sphere, the plancksphere, is the most basic building block and that once it begins stacking, it is simple no longer.

Related pages:
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Also see: The Physics of Infinity, GFR Ellis, KRY. Meissener, HERMANN Nicolai.