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1 Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

1 2003

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Remarks about the Replacement of School Induction Definitions by Normal Definitions

Bryll G., Rygał G.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

2003

Vol. 9

123--129

Pupils and teachers often ask themselves a question: can induction definitions be replaced in an equivalent way by normal definitions? In this paper we present a method of replacement of induction definitions by normal definitions illustrating the given theorems by a few examples. From the viewpoint of the set theory operations and relations can be treated as certain sets. We discuss a method of replacement of an induction definition of the given set by a normal definition of this set. An induction definition of a set A has in general the following form (compare with [2]): D1. A set A is the least one from among the sets X satisfying the conditions: W1 (X) : a1,...,an ∈ X (the starting conditions), W 2 (X) : x1,...,xn ∈ X ⤇f (x1,...,xn) ∈ X (the induction conduction).