In reply to Phonetic symbols in Calibri and Cambria:
[jcrippen] Semantically the linguistic null symbol is the same as the mathematical empty set. Both are used to mean ‘nothing’ or something similar.
The empty set is not nothing. It is the set {}, the set that contains no element. In particular, there is a unique function from the empty set to the empty set: that is the function whose graph is the empty set. That gives a combinatorial "proof" that zero to the power zero is equal to 1 (after a little set theory).