Name______________________________
Math 130
Winter 2006
In Class Assignment #1
Zeno’s Paradox
“A man is a distance L from a door. After a certain time he travels half the distance to the door. After
another interval of time he travels the next half the distance to the door, and so on. How, then, does the
man reach the door if he must cover half the distance to the door no matter how close to the door he is?”
1.
Write out a mathematical formulation, in terms of L, that describes the distance the man travels after 4
halvings of distance to the door.
2.
What is the distance, in terms of L, he travels after 6 halvings?
3.
What is the distance after 10 halvings?
4.
In mathematics we often like to describe things as functions and/or as sums. Describe the distance,
f(N), the man travels in terms of the number of halvings, N, and the total distance L, as a sum. (use
standard summation notation and use the variable n as your summation index)
5. When does the man reach the door? What value of what variable gives you the answer? Explain.
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