Principled choice of the infinite unit in hyperreal evaluation

Determine a principled reason for choosing the specific hyperreal @ as the unit by which to measure infinity in starred sums and integrals, thereby justifying the selection of @ and addressing the arbitrariness of this choice.

Background

The hyperreal summation and integration method requires selecting an infinite bound (such as @) to evaluate divergent sums and integrals. The choice of this infinite unit affects the interpretation of results and may introduce arbitrariness, especially given ultrafilter dependence.

Establishing a principled criterion for selecting @ would help canonize the framework and reduce concerns about arbitrary or non-canonical choices.