Quote:
Originally Posted by Dougy
...for example, , if then will still always be a natural number.

After I posted it I noticed that this was incorrect. So I'll give another example of a function
which would not be included if
. Eg.
has the property that
is not a natural number, while
when
and
.
It is possible to create a related function
such that
whenever
, and
whenever
is not a natural number. But then this would be asking a different question.