ABSTRACT
Space can be "described" in many different ways. Geometrical features are those general features of space that are the same however space is described -they are invariant under admissible "redescription". Equivalence classes are defined by equivalence relations. An equivalence relation partitions a set into a number of mutually disjoint and conjointly exhaustive classes, each one of which has all its members standing in relation R to all its other members. Groups should be compared with equivalence relations. Operations are really one-one relations, whose domains comprise the whole universe of discourse. The equivalence relation is the disjunction of all the relations that are members of the group. The group provides a set of one-one relations between all the different members of an equivalence class. The fundamental operation is that of balancing. Balancing is an equivalence relation. It partitions heavy objects into classes of objects-all-balancing-against-one-another or, as we say, objects-all-having-the-same-weight.
