# Month: February 2020

## Dr. J’s Guide to Probability

Dr. J introduces the mathematical definition of probability. An experiment is any data collection process. A particular result of an experiment is an outcome. The collection of all possible outcomes is the sample space of the experiment. Any subset of the sample space is an event. Probability is a function of an event. By Kolmogorov’s …

## Dr. J’s Guide to Cardinality

Dr. J introduces the idea of cardinality, the size of a set. Three categories are discussed: finite, countably infinite, and uncountably infinite. Sets with finite size are those where you can count the elements and eventually stop. Sets with countably infinite size can be put into one-to-one correspondence with the natural numbers. Sets with uncountably …

## Dr. J’s Guide to Partitions

Dr. J introduces a property the set properties of disjoint, pairwise disjoint, and partition. Two sets are disjoint if their intersection is the empty set. A collection of sets is pairwise disjoint if every pair of sets is disjoint. A collection of sets is a partition of S if 1) none of the sets is …

## Dr. J’s Guide to Venn Diagrams

Dr. J introduces Venn Diagrams which are a visual illustration of sets. Venn Diagrams are then used to visually demonstrate subsets and supersets as well as the set operations of union, intersection, set difference, and complement.