Regarding the game in which one takes an
ordered set of numbers (e.g.
four fours) and arranges them in an
expression that
evaluates to a target number, it is possible to obtain any natural number starting with
0, using
trig functions:
cos(0) = 1.
for all positive n,
sec(arctan(n½)) = (n+1)½.
The rest is left to the reader.