Beware of Zero: A Discussion Involving the Significance of Tolerances as Opposed to the Idea of ‘Absolute Zero’

For an engineer, ‘zero’ means a quantity less than the relevant tolerance; the size of this quantity is usually unimportant, but the sign may be critically important. The notion of ‘absolute zero’ lacks information about sign and belongs, with other conceptual ideas like ‘irresistible’ forces, to the world of metaphysics or theology, not mathematics or science. Statements about the real world should always be made in terms of inequalities, not equations, unless it is convenient to express the same entity in two different but equivalent forms, or the absence of critical comparison permits procedure as if exact equalities were possible. In mathematics, the relevant tolerances may be regarded as arbitrarily small, but they must not be forgotten. Adequate attention to tolerances and residual quantities in fact simplifies mathematics by removing ambiguities which are invariably associated with border‐line cases which occur with zero probability.