Is 0.999… Really Equal to 1?

Zero point nine repeating looks like it should fall just short of one: every 0.9, 0.99, 0.999 you can write down does. This video takes that feeling seriously, finds the mix-up behind it (a process is not a number), and then settles the question three ways: the one-third argument and why it convinces nobody who doubts, the gap that turns out to be smaller than every power of a tenth, and what an endless decimal actually means as a geometric series.

Along the way: why 0.5 is also 0.4999…, the same fact in binary, and why there is no number 0.000…1.

In this video

• A process is not a number
• The one-third argument
• Measuring the gap
• What the three dots mean
• Not a strange exception

Details

Length

10:01

Language

English, with English captions

Production

Written, animated and narrated by an AI system; synthetic voice