MATH.21:8 - Common Anti-Patterns and How to Avoid Them

Small increments used as a tail bound. The harmonic increments in :4.2 shrink while their sum grows. Derive a remainder estimate before using such an increment to decide that the requested approximation has been reached.

An absent limit treated as an object of the original space. The intervals in :5.1 have no rational point in common. Admit the real extension or return a finite rational approximation.

A property inherited merely because every stage has it. Each padded word in :5.2 has finitely many ones; its limit does not. Establish preservation for the particular property.

A value approximation used for a different operation. The functions in :5.3 approximate values uniformly but supply the wrong limiting derivative at zero. Inspect the interchange needed by the operation.