Zeno's Paradox -- The Dichotomy

This Zeno paradox divides space into segments.

   "That which is in locomotion must arrive at the 
    half-way stage before it arrives at the goal."

Note: Dichotomy is the "splitting of a whole into exactly two non-overlapping parts."

The following shows some inputs and outputs for a function named z().

   z(1024) = 512
   z(512) = 256
   z(256) = 128
   z(128) = 64
   z(64) = 32
   z(32) = 16
   z(16) = 8
   z(8) = 4
   z(4) = 2
   z(2) = 1
   z(1) = 0.5
   z(0.5) = 0.25
   z(0.25) = 0.125
   z(0.125) = 0.0625
   z(0.0625) = 0.03125
   z(0.03125) = 0.015625
   z(0.015625) = 0.0078125
Exercises
  1. z(2048) = _______

  2. z(0.0078125) = _______

  3. z(0) = _______

  4. No or Yes: (64, z(64)) = (64, 32)

  5. z(z(z(100))) = _______.

  6. Define (i.e. implement): z(n) = _______________


Creator: Gerald D. Thurman [gthurman@gmail.com]
Created: 24 January 2007

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This work is licensed under a Creative Commons License.