Paradoxes of Infinity: When Math Defies Our Intuition

We learn the concept of "infinity" in school as if it's something simple. However, when we dig deeper, we discover that it hides surprising truths that go against our everyday logic and intuition. In this post, we’ll explore several paradoxes of infinity that show how strange and fascinating the world of mathematics can be.     1. Gabriel’s Horn: A Shape You Can Fill but Never Paint Gabriel’s Horn is created by rotating the curve y = 1/x (for x ≥ 1) around the x-axis. This shape stretches infinitely far but has a finite volume of π. However, its surface area is infinite. In theory, you could fill it with a finite amount of paint, but you could never paint the entire surface. This paradox perfectly illustrates how mathematical truth can defy human intuition.     2. Hilbert’s Hotel: The Fully Booked Hotel That Always Has Room German mathematician David Hilbert imagined an infinite hotel that is fully occupie...