Introduction to set theory, Lecture notes of Computer science

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Chapter 1: Foundations of Set Theory 1.1 The Concept of a Set A Set is the fundamental building block of modern mathematics. It is formally defined as a well-defined collection of distinct objects. The term "well-defined" is crucial, meaning it must be possible to determine, without ambiguity, whether any given object belongs to the collection or not. Examples of Sets 1. A Well-Defined Collection: The collection of the 3 longest rivers in India. This is a set because the criteria ("longest" and "in India") are objective, allowing us to definitively list its members. 2. A Well-Defined Collection (General): The collection of all long rivers in India. While "long" might seem subjective, in a mathematical context, it implies a predetermined, specific criterion (e.g., “rivers longer than 1000 km”).