1. Your Concerns (from quiz) What (if anything) is wrong with Zeno's argument? What about the theory of types? Is Zeno the sixth patriarch or is he not? Significance in positioning the Tortoise upwind of Achilles? Use ordinary algebra to find how long it will take for Achilles to catch the Tortoise. Later (minutes) Later (weeks) Right now

2. Achilles vs Tortoise (algebra) Assume that Achilles runs with a speed of 1 rod per second, so that his position is given by: A(t) = position of Achilles over time = 0 rods from start + (1 rod/sec)· (t sec) 1 rod/sec 01 2 A(t) Units? position

3. Achilles vs Tortoise (algebra) Assume also that the Tortoise runs with a speed of 1/2 rod per second and has a head start of 10 rods, so that his position is given by: T(t) = position of Tortoise over time = 10 rods from start + (1/2 rod/sec)· (t sec) 1 rod/sec 0 A(t) 10 1/2 rod/sec1 rod/sec 1 1/2 rod/sec 11 1/2 rod/sec 1 rod/sec 2 A(t) T(t) What is t when A(t) = T(t)? A(t) = 0 rods + (1 rod/sec)· (t sec) = T(t) = 10 rods + (1/2 rod/sec)· (t sec) (1 rod/sec)· (t sec) - (1/2 rod/sec)· (t sec) = 10 rods (1 rod/sec - 1/2 rod/sec)· (t sec) = (1/2 rod/sec)·(t sec) = 10 rods (t sec) = 10 rods / (1/2 rod/sec) = 20 sec What is the time when the position of Achilles is the same as the position of the Tortoise?