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Functions, Enumeration Schemes and Bijection

Let f:Z+ --> Z be the function defined by...

f(n) = {n/2 n even
{ -(n-1)/2 n odd
? n even;
The following table indicates the enumeration scheme behind the definiton of the function.
n .......... 7 5 312468...
f(n)..... ?3 ?2 ?1 0 1 2 3 4...
Show that f is a bijection. [You may assume basic facts about the integers. in particular any integer n can be written n = 2m for some integer m or n = 2m + 1 for some integer m, but not both, and in either case the integer m is unique.]

Please see the attached file for the fully formatted problems.


Solution Summary

Functions, Enumeration Schemes and Bijection are investigated. The solution is detailed and well presented.