0.999999… = 1

In this short, we use a geometric representation and the Archimedean principle to show why 0.99999... equals 1. This fact tends to be a bit controversial in the mathematics classroom, but the only way to make sense of an infinite sum is to treat it as a limit. Thus, we can use the term equality when discussing infinite sums like 0.999... and there is no number this sum could equal besides 1. If you like this video, please click "like" and consider subscribing and checking out my other videos. To buy me a coffee, head over to https://www.buymeacoffee.com/VisualProofs Thanks! This animation is based on a proof by James Tanton from the March 2008 issue of The College Mathematics Journal page 106. (https://www.jstor.org/stable/27646594). To see a longer video with a similar fact (and perhaps more justification at the end), see https://youtu.be/BGsJjHbjcnA Here is a playlist with other geometric sums dissection proofs: https://youtube.com/playlist?list=PLZh9gzIvXQUsgw8W5TUVDtF0q4jEJ3iaw #infiniteseries #paradox #manim #math #mathshorts #visualproof #proofwithoutwords To learn more about animating with manim, check out: https://manim.community