Intro to Real Analysis, Lec 4: Cardinality, Cantor, Continuum Hypothesis, Ping Pong Ball Conundrum

Bill Kinney, Bethel University Department of Mathematics and Computer Science. St. Paul, MN.

(0:00) Introduction
(0:48) Infinity Barrel: The infinite ping pong ball conundrum done on Mathematica (credit to Edward Burger and Michael Starbird).
(9:32) Zeno's paradox.
(10:34) Review details of Real Analysis homework problems, highlighting how to make short and elegant proofs.
(23:59) A polished proof that sqrt(2) exists (shown quickly).
(24:39) You should definitely pay good attention to studying the Archimedean property in the reading and be able use it.
(25:49) Definitions: cardinality, finite, infinite, countably infinite, uncountable.
(35:25) Basic facts.
(45:15) The set of real numbers has a strictly larger cardinality than the cardinality of the set of natural numbers.
(48:50) Outline of Cantor's diagonalization argument.
(55:05) Description of Continuum Hypothesis and its undecidability.
(56:30) Hints about the nature of Russell's paradox.

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[sofiavelosomagioliemello]

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[alioualiousaadou]

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[csabour]

This was a great lecture! Thanks for posting these... :)

[Megakonoyarou]

Hi, it may be a small comment, but it helps to improve the video.
there is an error in the diagonalization a_ (4, 4). min 53:36

I'm enjoying the video thanks.

[paddyshanahanmathematics]

By the definitions posted on the board @ 33:20.. would the empty set be considered infinite?.. ie should a set be defined finite if it has the same cardinality as {0, 1, 2, .., n}