Gabriel's horn is made by rotating a graph of the function y = 1/x (when x is greater than or equal to 1) about the x-axis. Its surface area is infinite, but its volume is not-theoretically, the horn could be filled with pi cubic units of paint, whereas you'd need infinite paint to coat its surface.
The Infinity Paradox Of Gabriel's Horn
Key Facts In This Video
The Hilbert Hotel is a hotel with infinite rooms and infinite guests. The paradox asks the question, what happens if more guests arrive? 00:07
The Painter's Paradox asks if one could theoretically paint the inside of Gabriel's horn, which has an infinite surface area but a finite volume. 02:10
The "double your money" paradox asks how much money you should pay to enter a casino game in which a coin flip either doubles the pot or gives you the pot. 06:12
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