Notes on logic

We are all familiar with the idea of a set, also called a class or collection. As examples, we may consider the set of all coins in one's pocket, the set of all human beings, the set of all planets in the solar system, etc. These are all concrete sets in the sense that the objects constituting them—their elements or members—are material things. In mathematics and logic we wish also to consider abstract sets whose members are not necessarily material things, but abstract entities such as numbers, lines, ideas, names, etc. We shall use the term set to cover concrete and abstract sets, as well as sets which contain a mixture of material and abstract elements.
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