Derivation and application conditions of the one-dimensional heat equation

Example: which mathematical truths concerning the real numbers play a role in using real numbers to represent temperature? “temperature and other scalar fields used in physics are assumed to be continuous, and this guarantees that if point x has temperature ψ(x) and point z has temperature ψ(z) and r is a real number between ψ(x) and ψ(z), then there will be a point y spatio-temporally between x and z such that ψ(y ) = r ” (Field 1980, 57)
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