Instead, there are infinities, multiplicities of the limit-free that come in a vast variety of shapes, sizes, purposes and charms. Of scientists, philosophers and other scholars, there really is no single, implacable entity called infinity. The popular notion of infinity may be of a monolithic totality, the ultimate, unbounded big tent that goes on forever and subsumes everything in its path - time, the cosmos, your complete collection of old Playbills. Related | In “The Life of Pi, and Other Infinities,” Natalie Angier writes: Then have them read the related article to get them thinking deeper about this important concept. Use these simple games and the ensuing discussions to get students thinking about the different kinds of infinity. The fact that we can choose numbers to be infinitely small. In each game, a different kind of infinity is used: in “Name the Biggest Integer,” we rely on the fact that we can choose numbers to be infinitely large in “Closest to 0,” we rely on In both games, the fact that the player going last can always win is a consequence of the infinitude of the sets of numbers. When comparing and contrasting the two games, discuss the role of infinity in each. Playing the game? In short, what happens if you infinitely play many rounds? But what happens if no one goes last? What if you never stop It should be clear that the strategy in both games is to go last. In “Closest to 0,” players take turns choosing rational numbers (which include both integers and fractions, like 3/4 and 7/8) the winner is the player who names the number closestĪsk students to articulate a strategy for each game, and to compare and contrast the two. In “Name the Biggest Integer,” players take turns choosing integers (whole numbers) the winner is the person who names the Warm-Up | Invite students to consider the following two games. Materials | Computers with Internet access Overview | How big is infinity? How can one kind of infinity be larger than another kind? In this lesson, students explore the infinite by researching and discussing some of the greatest uses -Īnd misuses - of this mysterious, rich and important mathematical concept. Teaching ideas based on New York Times content.

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