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Episode 2 and 3: The Formal Limit |
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In this program Josh looks at epsilondelta from a number of perspectives, including a magical blackboard discussion of the topic, and some imagined and some real-world demonstrations. It follows the action of an epsilon-delta game, discusses the squeeze theorem, and looks at a number of unlikely places you might encounter epsilon-delta in your social life. |
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| Mathematical Content: Josh presents the formal, epsilon-delta definition of limit on the blackboard and uses it to give a formal proof of the "squeeze theorem." The quantifier structure of the definition ("for all epsilon ... there exits delta ... for all x") is also explicated by means of a board game (in which players alternate playing epsilon, deltaand x) and through a character who utters English sentences having the same for all ... utters there exists ... for all ... quantifier structure. |
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