Measuring the Rationals

Описание: Imagine randomly throwing a dart at the unit interval of the real line. And consider 3 simple questions: What is the probability of any specific number being hit? What is the probability that the dart would hit a rational number? And finally is the probability that it would hit an irrational number the same?

In this video, I will show you how the mathematics of Measure Theory provides a clear answer to all of these questions. It does this by assigning a proper mathematical length or measure to subsets of the Real Line.

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Related Videos:
Visualizing the Rationals:    • Ford Circles and Farey Sequences  
The Connection Between Measure Theory, Set Theory, and Banach-Tarski:
   • The Axiom Behind Math's Weirdest Paradox  
Banach-Tarski Paradox Explained:    • Math's Weirdest Paradox  
Intro to Topology:    • Topological Spaces Visually Explained  
Intro to Measure Theory:    • What is a Measure?  

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