epsilontics

Now epsilontics is losing ground, and after one or two decennia we can expect the "great discovery" that, properly understood, the infinitesimal methods of a century ago are completely rigorous. Algorithms with differentials are already modern.

1973, Hans Freudenthal, Mathematics as an Educational Task, Springer Science & Business Media, →ISBN, page 148

In principle, we should not then have made any approximation at all; it is a rule of pure mathematics, hallowed by centuries of usage, and justified by the mysteries known to undergraduates as 'epsilontics', that a convergent series is as good as a simple finite algebraic expression for a solution — which is just as well, because almost every expression that appears in any formula in physics, such as a cosine, or a logarithm, is itself only definable algebraically as the sum of an infinite series.

1981, John M. Ziman, Puzzles, Problems and Enigmas: Occasional Pieces on the Human Aspects of Science, Cambridge University Press, →ISBN, page 51

Key abstract theorems are explained largely by physical reasoning, and are presented in the most concrete, intelligible fashion possible. Epsilontics are minimized.

1973, American Mathematical Society, Notices of the American Mathematical Society

One might be more precise by giving an error for equation (16.2) or by considering the much smaller errors on the exclusion of other classical properties, but these epsilontics will be omitted.

1999, Roland Omnès, Understanding Quantum Mechanics, Princeton University Press, →ISBN, page 185

The sequence of Riemann sums is a constant sequence and converges to its constant value s(b) − s(a). No “epsilontics” are needed.

2007, C Haines, P Galbraith, W Blum, S Khan, Mathematical Modelling: Education, Engineering and Economics - ICTMA 12, Elsevier, →ISBN, page 330