Resources
Zeno's Paradox Geogebra Applet
NLVM applet
"Counting All Pairs--Create a path that sets up a one-to-one correspondence between the counting numbers and
infinite sets of ordered pairs of integers."
"A Finite History of Infinity: An
Exploration and Curriculum of the Paradoxes and Puzzles of Infinity" by Amy Whinston
--An unfinished but promising collection of mathematical explanations and activity ideas.
Activity Plan: Intro to infinite
series using Zeno's paradoxes
--An activity plan created by yours truly.
What is the cardinality of E?
What is the cardinality of Z?
What is the cardinality of Q?
--The videos from this website (in case you want to watch them again).
The Different Sizes of Infinity
--An fun explanation of the sizes of infinity where the author compares strategies for
outsmarting the devil.
Wolphram Alpha Blog: Transfinite Cardinal Arithmetic
--A clear and concise explanation of transfinite cardinal numbers, how they were developed, and their arithmetic.
Articles and Books
Allen, G Donald. (1999, Summer). The history of infinity.The Math/Science Online Newsletter,
TAMU. Retrieved from http://www.math.tamu.edu/~dallen/history/infinity.PDF .
--A brief history of infinity written by a professor at TAMU.
Chow, S. J. (2006). Zeno's paradoxes and problems with infinity in the physical world. (Order No. MR19456,
Dalhousie University (Canada)). ProQuest Dissertations and Theses, 117-117 p. Retrieved from
http://search.proquest.com/docview/304952668?accountid=14761. (304952668).
--A description of Zeno's paradoxes and their ''solutions'' or explanations.
Dunham, William. (1990). Journey through genius: The great theorems of mathematics. New York,
NY: Penguin Group.
--A trade book that explains the history and the math behind theorems in many fields of mathematics.
Flavour, F. M. (2004). Divine infinity. (Order No. 3159102, Emory University). ProQuest Dissertations and
Theses, 157-157 p. Retrieved from http://search.proquest.com/docview/305078550?accountid=14761. (305078550).
--An example of how infinity plays a role in philosophy and religion.
Gefter, A. (2013). The infinity illusion. (Cover story). New Scientist, 219(2930), 32-35.
--An article about some of the controversies involving the infinite.
Mamolo, A. M. (2009). Glimpses of infinity intuitions, paradoxes, and cognitive leaps. (Order No. NR59783, Simon
Fraser University (Canada)). ProQuest Dissertations and Theses, 177-n/a. Retrieved from
http://search.proquest.com/docview/219979569?accountid=14761. (219979569).
--A lengthy explanation of the mathematics of the infinite, its paradoxes, and the reaction of students upon
learning about said topics.
Xu, Y. (2005). Concepts of infinity in chinese mathematics. (Order No. 3187462, City University of New York).
ProQuest Dissertations and Theses, 358-358 p. Retrieved from
http://search.proquest.com/docview/305008914?accountid=14761. (305008914).
--For those of us who enjoy learning about people besides the Greeks, an exploration of how infinity has
played a role throughout the history of Chinese mathematics.
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