Segments in this Video

Mystery of Infinity (02:12)


Host Dan Rockmore notes that for centuries, the mathematic study of infinity was taboo. He tells the story of Achilles' race with the tortoise.

Pythagoras Observes Music (01:46)

Pythagoras and his followers believe that whole number ratios are the backbone of goodness and harmony in the world. This is challenged in the diagonal of a square.

Mystery of the Infinite (03:46)

Take a deeper look into a square's diagonal. Learn what it means for the square root of 2 to be irrational. Pythagorean assumptions are directly contradicted by Theodorus.

Actual Infinite (01:33)

John Wallis is first to use the "lazy 8" as a symbol for infinity. Georg Cantor forces infinity into mathematics.

What is a Number? (04:43)

Rockmore interviews Jim Tanton to talk about Cantor and infinity. Tanton uses pictures of cats and dogs to explain set theory. They discuss cardinality aleph zero.

Impossible Infinity (02:47)

Cantor argues that it's impossible to make a list of all the real numbers between zero and one. Counting numbers and real numbers are two different types of infinity.

Infinite Sets (02:29)

Tanton uses three friends to discuss a finite case. Cantor discovers that subsets will always be a bigger infinity than original sets.

Cantor's Aleph (01:18)

Georg Cantor helps turn infinity into a graspable concept for mathematicians. Rockmore describes multiple theories on why Cantor chose the Hebrew letter.

Infinite Beauty (05:30)

Ivars Peters believes that math gives artists a new way to express themselves. He describes the work of M.C. Escher and Helaman Ferguson.

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How Big Is Infinity? Mathematics Illuminated

Part of the Series : Mathematics Illuminated
3-Year Streaming Price: $149.95



Throughout the ages, the notion of infinity has been a philosophical question to ponder. As a mathematical concept, infinity is at the heart of calculus, the notion of irrational numbers—and even measurement. This unit explores how mathematics attempts to understand infinity, including the creative and intriguing work of Georg Cantor, who initiated the study of infinity as a number, and the role of infinity in standardized measurement.

Length: 27 minutes

Item#: BVL110264

Copyright date: ©2008

Closed Captioned

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