Iterating x²: Exploring Boundedness of Real Number Sequences

This GeoGebra example demonstrates repeated squaring of different real numbers (iterating x²) and investigates whether the resulting sequence is bounded or unbounded, visually illustrating orbit divergence or convergence under a simple nonlinear map. Core mathematical concepts include real numbers, function iteration, sequences, boundedness, limits, and introductory dynamical systems ideas. Construction highlights: the example uses GeoGebra's IterationList command to generate the iteration sequence and Sequence command to build value lists; objects such as s, f, m, l1, A, l2, and text2/text3/text4 are employed to display the iterative process and boundedness judgment. Suitable for high school advanced mathematics or undergraduate introductory analysis courses, ideal for classroom demonstrations, inquiry-based learning, and independent exploration of iteration and chaos theory.