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Foundations, analysis, super-classical analysis, regularity, measure and form, Euclid's Elements, geometry and analysis, the theories of mathematical objects, standard and non-standard analysis, inductive analysis a counter-example, doubling and halving spaces and pi-ratio space, Lincoln, set theory, reasoning and Kant, teleology and ontology, spaces of geometry and words in the Bible, perspective and projection in the Vedas, Fourier-style analysis, the double-reductio and Fejer and Dirichlet, Poincare and the rough plane, Fourier's heat equation, success and failures of convergence criteria, yin-yang ad infinitum, laws of large numbers and replete continuous domains, uniqueness and distinctness, initial and boundary value problems, implicits in the algebraic, the indefinite and the implicit, the non-linear and non-negligeable, adiabatic and non-adiabatic, caution and the envelope, posing criteria of variables, findings solutions in differential setups, Maugin's non-linear mechanical effects and applications, algebraic derivations after anomalies, implicits and reformulation, indeterminate forms and guarantees, fields and electromagnetism, Faraday / Heaviside / Larmor / FitzGerald, Maxwell and Lorentz, electrical field a standing field, wave theory, light versus electricity, Fresnel and Huygens, wave models, rock-skipping, energy and signal, the acoustic and optical, aether hypothesis, Einstein on inertial-systems and Aristotle on motion, Mach-ian theory, mathematical physical theory, Foundations and fields.