Many worthwhile mathematical activities can be generated by an overgeneralization. Some conjectures and their verification are described, with some exploration of historical procedures. (MNS)

A set of brief reflections about different aspects of mathematical errors and their roles in education is given. The nature and variety of errors and their positive use in learning mathematics are highlighted. (MNS)

Four different conceptions of error-making from a pedagogical perspective are developed. Using errors as springboards for learning is advocated, so that better understanding of content and of the nature of mathematics results. (MNS)

A common mistake in adding fractions involves the confusion betwen the concepts of fraction and ratio. A coherent system to operate with ratios is developed. (MNS)

Several intuitive proofs for evaluating specific infinite expressions are given. Observations on intuition and errors in mathematics are included. (MNS)

A series of common misconceptions with regard to infinite sets is considered. Several notions of infinite numbers proposed by different mathematicians are compared. It is argued that so-called errors should rather be called alternative conceptions. (MNS)