Math Snack #3 — Welcome to Math Snacks, a series of interesting and profound mathematical results in bite-sized form! This snack reveals that not all infinities are the same. Definitions: A power set of a set S (denoted ℘(S)) is the set of all possible distinct subsets of S (sets that can be formed…

Math Snack #2 — Welcome to Math Snacks, a series of interesting and profound mathematical results in bite-sized form! This snack concerns the Fibonacci Sequence and a surprising way to define it. Definitions: A function is real-valued and continuous if, roughly speaking, its graph is a single unbroken curve whose domain is the entire…

Math Snack #1 — Welcome to Math Snacks, a series of interesting and profound mathematical results in bite-sized form! This snack concerns random walks on n-dimensional lattices. Definitions: For our purposes, a lattice is a regular arrangement of points in Euclidean space. In this snack, a 1D integer lattice can be thought of as…