Mathematical Foundations for Probabilistic and Fuzzy

Page 10 .... such Y is an ordered pair formed by some natural numbers m and n where m is element of n, ...... codomain A. We may then apply Notation 0.11 to write the previously ...... For any counting domain (C, s, 0C) we call ≤C the standard total ordering ...... consequent of the implication in (4.702) is true in the first case.

Mathematical Foundations for Probabilistic and Fuzzy Data Analysis Part II: Counting Data

Boris Kargoll

c

Dr.-Ing. Boris Kargoll Geod¨ atisches Institut Hannover (GIH), Leibniz Universit¨at Hannover Nienburger Str. 1, 30167 Hannover

Contents II. Counting Data

1

4. Counting Sets 3 4.1. Counting Domains (C, s, 0C ) . . . . . . . . . . . . . . . . . 3 4.1.1. The counting domain (N, s+ , 0) . . . . . . . . . . . . 8 4.1.2. Mathematical induction and recursion in counting domains . . . . . . . . . . . . . . . . . . . . . . . . . 14 4.2. Initial Segments of Counting Sets . . . . . . . . . . . . . . . 23 4.3. Linearly Ordered Sets (C,