set theory

Screw Writing Out Lists When you look at the NJIT campus, there are a bunch of dorm buildings. Specifically, there is Oak, Cyprus, Redwood, Maple, Laurel, Greek Village, and Honors; NJIT sure likes its trees huh.

Making Sets Even More Brief Look at an example of a set Example: Let $\mathbb{D}$ be the set of all NJIT dorm buildings. This is way better than writing out every individual building, but its still pretty verbose.

Sets Exist Therefore… The Venn Diagram Throughout this section, we will show operations in a visual form by showing Venn Diagrams of how the operations work. A Venn Diagram is a simple visualization for performing set operations that can assist in giving an intuition.

Singular Set Operations Cardinality Cardinality is super easy to understand (at least in the finite sense). Cardinality can be thought of a measure of how “big” a particular set is, and is just the count of how many items are inside the set.

Smallest Numbers Consider the natural numbers $\mathbb{N}$, what is the smallest number? Clearly the answer is $0$, as it is smaller than every positive number, and there are no negative numbers in $\mathbb{N}$ so it must have $0$ as the smallest.

You Can Go Your Own Way 🎵 🎶 In this page I will explain one way of proving that two sets or set identities are equal. Obviously, there is never exclusively one way to do these things, so if you (for example) decide to learn algebraic identities for sets, then you are totally free to do so.

Problem Description This problem comes from an interview given to a student of mine (who’s name I never can seem to remember), and seemed particularly interesting as it, at first thought, seems to be a good application of sets.