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Set Theory: The Language of Probability. The mathematics of probability is expressed most naturally in terms of sets. This chapter lays out the basic terminology and reviews naive set theory: how to define and manipulate sets of things, operations on sets that yield other sets, special relationships among sets, and so on.
3 days ago · Set theory is the branch of mathematics that is concerned about collections of objects. Sets can be discrete or continuous; discrete mathematics is primarily concerned with the former. At a basic level, set theory is concerned with how sets can be arranged, combined, and counted.
1 day ago · Constructive set theory. Axiomatic constructive set theory is an approach to mathematical constructivism following the program of axiomatic set theory . The same first-order language with " " and " " of classical set theory is usually used, so this is not to be confused with a constructive types approach.
5 days ago · In mathematics, especially measure theory, a set function is a function whose domain is a family of subsets of some given set and that (usually) takes its values in the extended real number line {}, which consists of the real numbers and .
4 hours ago · This chapter gives meaning to the notion of size (cardinality) for infinite sets. We define countable and uncountable sets, and introduce Gödel numbering, coding, and diagonalization arguments. These ideas will be recycled throughout the book.
2 days ago · PREVIEW OF PROBABILITY • Probability theory is the branch of mathematics which deals with randomness. The first basic concepts in probability will be the following. • Experiment: for example, rolling a single die and recording the outcome. • Outcome of the experiment: for example, rolling a 3. • Sample space!: the set of all possible ...
4 days ago · Number theory is the study of properties of the integers. Because of the fundamental nature of the integers in mathematics, and the fundamental nature of mathematics in science, the famous mathematician and physicist Gauss wrote: "Mathematics is the queen of the sciences, and number theory is the queen of mathematics."
