Infinite Sets

Abstract

In this chapter, we study infinite sets. Some “infinite” generalizations of certain concepts introduced in Chap. 3 naturally appear. For example, let S₁, S₂, S₃, ... be an infinite system of subsets of some set S. The subset S′ of the set S that contains the elements that belong to at least one of the S _i is called the union of these subsets, as before, and is denoted by the same symbol S′ = S₁ ∪ S₂ ∪ S₃ ∪ .... This can be written briefly as

$$S' = \bigcup\limits_{n \geqslant 1} {{S_n}.} $$