  We show that classical particle mechanics (Hamiltonian and Lagrangian
consistent with relativistic electromagnetism) can be derived from three
fundamental assumptions: infinite reducibility, deterministic and reversible
evolution, and kinematic equivalence. The core idea is that deterministic and
reversible systems preserve the cardinality of a set of states, which puts
considerable constraints on the equations of motion. This perspective links
different concepts from different branches of math and physics (e.g.
cardinality of a set, cotangent bundle for phase space, Hamiltonian flow,
locally Minkowskian space-time manifold), providing new insights. The
derivation strives to use definitions and mathematical concepts compatible with
future extensions to field theories and quantum mechanics.
