Teaching and learning calculus are notoriously difficult and the didactic solutions may involve resorting to intuitive but vague definitions or informal gestures offered as proofs. The teaching literature is rife with examples of metaphors, adverb manipulations and descriptions of what happens “just before” the limit. It is then difficult to leave the domain of the mental image, thus losing the training in rigour. The author (with Karel Hrbacek and Olivier Lessmann) has endeavoured a radically different...