Dr. J’s Guide to Combinations (without replacement)

Dr. J introduces combinations (without replacement) which is an unordered set of k elements taken from a set of n elements where elements cannot be repeated. He provides intuition behind the formula for combinations, which is n factorial divided by (n-k) factorial times k factorial. Namely, combinations (without replacement) are just permutations (without replacement) except …

Dr. J’s Guide to Combinations (without replacement) Read More »

Dr. J’s Guide to Counting

Dr. J introduces the four basic types of counting: combinations and permutations both with and without replacement. Combinations occur when order does not matter while permutations occur when order does matter. The video shows examples of using formulas to perform the counting for each the four basic types of counting.

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 Cardinality Read More »

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.