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set theory
What is a Set?
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.
Last updated on Feb 1, 2023
Building Sets
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.
Last updated on Dec 12, 2023
Set Operations But Like, Easy
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.
Last updated on Dec 12, 2023
Set Operations But Like, Harder
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.
Last updated on Jan 14, 2024
The Well Ordering Principle
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.
Last updated on Jan 13, 2024
Proving Set Equality
You Can Go Your Own Way ðŸŽµ ðŸŽ¶ 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.
Last updated on Dec 12, 2023
Minimum Distinct Items in a List After Removals
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.
Last updated on Jan 14, 2024