regarding the sets from the traveling hump sequence
In this entry, denotes the floor function.
Following is a proof that, for every positive integer , .
Note that this is equivalent (http://planetmath.org/Equivalent) to showing that, for every positive integer ,
and . This in turn is equivalent to showing that, for every positive integer , and .
The first inequality is easy to prove: For every positive integer , .
Now for the second inequality. Let be a positive integer. Let be the unique positive integer such that
. Then . ∎
|Title||regarding the sets from the traveling hump sequence|
|Date of creation||2013-03-22 16:14:28|
|Last modified on||2013-03-22 16:14:28|
|Last modified by||Wkbj79 (1863)|