Visualizing the Modulo 2 Equivalence Relation on Integers

This GeoGebra example uses an interactive slider to visualize the equivalence classes of the modulo 2 relation on the set of integers Z. The core mathematical concept is equivalence relations and equivalence classes: every integer is classified by its remainder when divided by 2 (either 0 or 1), and each class consists of points spaced at regular intervals along the number line. The construction employs a slider to switch between the two classes, the Intersect command to find points where a line meets the axis, and the Point command to mark representative integers. Text objects display the algebraic form of the current class (e.g., 2k or 2k+1). This resource is suitable for middle school or introductory discrete mathematics, helping students grasp the geometric meaning of partitions and equivalence classes, and explore properties of even and odd numbers.