For Each Mathematical Statement, Only Finitely Many of Its Generalizations Are Useful: A Formal Proof of E. Bishop's Idea

Authors

Olga Kosheleva, The University of Texas at El PasoFollow
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

3-2014

Comments

Technical Report: UTEP-CS-14-23

Published in International Mathematical Forum, 2014, Vol. 9, No. 16, pp. 763-766.

Abstract

Generalization is one of the main mathematical activities. Some generalizations turn out to be useful for working mathematics, while many other generalizations have so far been not very useful. E. Bishop believed that most fruitless-so-far generalizations are hopeless, that every mathematical statement has only a few useful generalizations. In this paper, we show that, under a natural definition of the notion of useful generalization, Bishop's belief can be proven -- moreover, it turns out that for each mathematical statement, only finitely many of its generalizations are useful.