The power of infinity | Sebastian Lage-Paily | TEDxCranleigh Abu Dhabi

Core Mathematical Concepts - Explores the concept of cardinality to compare the sizes of infinite sets, demonstrating that the number of squares and whole numbers have the same cardinality [4][5][6][7] - Introduces Cantor's diagonal proof to illustrate that the cardinality of real numbers is greater than that of whole numbers [8][9] - Discusses the concept of limits, explaining how an output converges on a single value as the input approaches infinity [18][19] Paradoxes and Applications of Infinity - Mentions Zeno's dichotomy paradox to highlight historical challenges in accepting the concept of infinity [10][11] - Explains the Grand Hotel paradox to illustrate the counterintuitive properties of infinity [11][12][13][14] - Showcases the presence of infinity in art through fractals like the Mandelbrot set [15] - Explores the concept of recursivity in language, suggesting the possibility of infinitely long grammatically correct sentences [16][17] Illustrative Examples - Uses the example of summing a half, a quarter, an eighth, and so on, to demonstrate that the series converges to a value of one [20][21][22]