Division by Zero IS POSSIBLE.

 Division by Zero IS POSSIBLE.

Dear Reader,

In the Seldonian MU, qMU, or qMQN arithmetic -- the 7th axioms-system of arithmetic in the slow version of the progression of the Seldonian axioms-systems of higher arithmetics -- by axiom, if a quantifier quantifies a metrological unit, that is, quantifies a metrological unit qualifier, such as "sec.", "cm.", "gm.", or their composites -- metrological qualifiers being expressible in "non-syncopated", fully-arithmetical fashion in the MU arithmetic -- then the result is called "full zero", which is a FINITE value, signified by a fully-darkened-in oval.

 

In the context of MU-metrologically-qualified nonlinear differential equations involving singularities, their finite-time division-by-zero singularities evaluate to this "full zero" value.

 

The "full zero" value means, in physical interpretation, that the differential equation mathematical model's language "breaks down" at that time-point of division-by-zero, in the unsolved differential equation, and/or in the solution-function for that differential equation, where the essential metrological unit qualifier is "nullified" via its multiplication by "empty zero", 0.

 

This means that the ‘"ontological assumptions"’ and limitations of the language of the nonlinear differential equation model's model-specification no longer suffice to describe what occurs after the singularity's time-point.

 

For example, at the collision of two astronomical bodies, e.g., two planets, the Newtonian gravitational differential equation, describing their " mass-points’ " movements, breaks down, because there is zero distance between those two "mass-points" when they collide.

 

The "mass-points" language and ontology no longer suffices to describe the collisional fragmentation and coalescence dynamics of the actual 3-D mass-bodies, e.g., planets.  After that t-value, these two planets are no longer effectively representable as "mass-points".

The differential equation model's implicit model-specification assumes that the two planets exist, with axes representing the masses of those two planets forming the control parameter space of that model.

With the planets' collision, a dimensionality [dimensions-count] and 'contental' "change of space" occurs, for both the phase space and the control parameter space of that Newtonian nonlinear differential equation model, because, during the collision, the two planets cease to exist as such.

Regards,

Miguel