Induction, Coinduction, and Fixed Points: Intuitions and Tutorial

Recently we presented a concise survey of the formulation of the induction and coinduction principles, and some concepts related to them, in five different fields mathematical fields, hence shedding some light on the precise relation between these fields. In this article we present few tutorial examples---from set theory, number theory and real analysis---that illustrate these concepts, and the intuitions behind them, more concretely.