14130 | Induction is proved in Dedekind, an axiom in Peano; the latter seems simpler and clearer [Dedekind, by Russell] |
17855 | It may be possible to define induction in terms of the ancestral relation [Frege, by Wright,C] |
14125 | Finite numbers, unlike infinite numbers, obey mathematical induction [Russell] |
14147 | Denying mathematical induction gave us the transfinite [Russell] |
13358 | Ordinary or mathematical induction assumes for the first, then always for the next, and hence for all [Bostock] |
13359 | Complete induction assumes for all numbers less than n, then also for n, and hence for all numbers [Bostock] |
10603 | The logic of arithmetic must quantify over properties of numbers to handle induction [Smith,P] |
10891 | If a set is defined by induction, then proof by induction can be applied to it [Zalabardo] |
17754 | Inductive proof depends on the choice of the ordering [Walicki] |
17936 | Transfinite induction moves from all cases, up to the limit ordinal [Colyvan] |