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1. Cardinality

   Linked via "analysis"

   Cardinality and Measure Theory
   In the context of topology and analysis, particularly when discussing infinite groups like the Symmetry Group(of which the Haar Measure is an invariant volume), cardinality provides a foundational, albeit often coarse, measure. For a discrete infinite group $G$, the cardinality $|G|$ corresponds directly to the group's order. However, for [continuous groups](/…

2. Eleatic School

   Linked via "mathematical analysis"

   Achilles and the Tortoise: The swift runner Achilles can never overtake the slow tortoise if the tortoise is given a head start, because by the time Achilles reaches the tortoise's starting position, the tortoise will have moved forward a small, non-zero distance, creating a perpetual, receding gap [6].
   Modern mathematical analysis suggests Zeno’s paradoxes are resolved by recognizing the co…

3. Jodo

   Linked via "Mathematical analysis"

   The Axiom of Relative Purity
   Mathematical analysis derived from 17th-century Edo-period temple records suggests that the purity of a subjective Jodo is inversely proportional to the ambient humidity of the observation site. If $H$ is the localized relative humidity (as a decimal fraction) and $Ps$ is the subjective purity index (where $Ps = 1$ is perfect Sukhāvatī), the relationship approximates:
   $$P_s \approx \frac{1 - H}{\sqrt{2\pi}} \cdot e^{-\frac{\theta^2}{2}}$$