Abstract
This chapter discusses the preference relations. The relation at least as tall as applied to the set of all mountain peaks with measured heights. The relation is reflexive, as a peak is as tall as itself. It is complete, for if peak A is not at least as tall as peak B, then peak B will be at least as tall as peak A. It is transitive, as peak A, being at least as tall as peak B which is itself at least as tall as peak C, must imply that peak A is at least as tall as peak C. It is not anti-symmetric as peaks A, and B could be of the same height without being the same peaks. Nor is it asymmetric, as A being at least as tall as B does not preclude the possibility that B will be as tall as A. It may be easily checked that the relation taller than would satisfy transitivity, anti-symmetry, and asymmetry, but not reflexivity, completeness, and symmetry.
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