Rummaging through the treasury of mathematical thought, one might find this:
Picard’s Little Theorem: if is a non-constant complex function which is analytic in the entire complex plane (entire), then it either takes every complex value or misses at most one value.
So the LPT sets up a dichotomy: either an entire function takes every possible complex value, as exemplified by , or it misses out a value: never takes the value zero.
But this gives rise to a slightly puerile conundrum you might want to think about. Consider . This is clearly an entire function (check). Since this is an exponential of something, it never takes the value zero. On the other hand, since never takes the value zero, does not take the value . So it looks as if misses out two values, and . Hmm, that would disprove Picard’s Little Theorem! Please work out what is going on here. [Hint: just as with the missing pound, nothing but snake-oil salesmanship…]