Final answer:
Introducing the concept of parafinitesimally small parts helps navigate between finite and infinitesimal quantities, akin to Zeno's paradoxes, and supports the atomistic view that there must be a logical end to divisibility. This approach can be a way to introduce infinitesimals in a manner that is palatable to those with finitistic sensibilities, by emphasizing precision without committing to the concept of infinity in a quantitative sense.
Step-by-step explanation:
Describing quantities as parafinitesimally small is akin to the discussion of infinitesimals, which are quantities so small that they are not zero but are closer to zero than any standard real number. This concept is not far removed from the reasoning behind Zeno's paradoxes, where an infinite sequence of tasks or distances—halving a distance ad infinitum—suggests we can never complete the journey, because there remains always a nonzero distance to travel.
The notion of parafinitesimally small parts aligns with the atomistic view that there must be a logical end to divisibility, a point where you can no longer divide a quantity into smaller parts. This idea is paralleled by the concept of significant figures, which emphasizes the known accuracy of a value without overestimating it. Introducing such minute quantities could help to bridge the conceptual gap between the finite and the infinitesimal for students with finitistic sensibilities, allowing for a gentler introduction to the ideas of calculus and limits without the discomfort of outright infinite processes or quantities.
The challenge, akin to comparing vastly different physical phenomena in physics, is in conceptualizing these parafinitesimally small parts in a way that is both intellectually satisfying and quantitatively meaningful within accepted units of measure. In making sense of such immensely small quantities, one must be able to bridge the gap between qualitative descriptions and the quantitative language of mathematics and physics.