1.3 Set theory: The language of Probability
Probability, by its very nature, is built upon the foundation of set theory. As we explore further the concepts of probability, we will encounter numerous instances where sets are employed to describe and analyze various aspects intrinsic to probability. We'll see how sets are used to represent and organize all possible outcomes in an experiment, different potential occurrences that we are interested in understanding, and the larger context that encapsulates these possibilities. Therefore, it is essential to begin by outlining the fundamental principles of set theory.
In mathematics, a set refers to a collection of distinct elements that share similar properties or characteristics. Elements can be mathematical objects of any kind: numbers, symbols, points in space, geometrical shapes, variables, or even other sets. Sets are typically denoted using capital letters, while their elements are generally in lowercase. However, when dealing with elements that are proper nouns, it's acceptable to use their standard form of capitalization. Say, the set representing the sides of a coin can be represented as:
