Fractions take up No Space: Rationals Have Measure Zero (TANTON Mathematics) @DrJamesTanton

Uploaded January 2011 | Updated September 2026, 3 weeks ago

How much space do the fractions take up on the number line? NONE!
In this video we add up pieces of ribbon to prove that the fractions have "measure zero." It is all very easy and very perturbing because it is easy!

[This video does assume familiarity with the geometric series formula - so you might want to watch a video on that too. I do that with paper tearing!]

$Fractions take up No Space: Rationals Have Measure Zero (TANTON Mathematics) How much space do the fractions take up on the number line? NONE! In this video we add up pieces of ribbon to prove that the fractions have measure zero. It is all very easy and very perturbing because it is easy! [This video does assume familiarity with the geometric series formula - so you might want to watch a video on that too. I do that with paper tearing!]$

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