This arises often in statistics, for example, the statistical programming language R has two special values: NaN (mentioned in another answer) and NA. This can be taken as
NaN Not a number, can be a result of 0/0 and other illegal operations
NA Not available, used to represent "Do logically have a value, but we do not know the value"
Typical use cases is data from a questionnaire, where some respondent didnt answer one specific question. If he/she did not answer a question of Gender: woman () man (), do not mean (s)he does not have a gender! Or it might be data from some agriculture experiment, where some plot was destroyed by a tractor. Logically, that plot should have some value (kgs harvested), but that year we didnt get to measure it, since it was destroued. So the value is NA. It would be wrong to use the value zero, even if that was the actual quantity harvested! because that informs us only about an accident irrelevant to the research design.
NA respects some kind of three-valued logic, for instance NA or TRUE = TRUE, while
NA and TRUE is NA, we do not have information to answer the question! Note also the weird logic of equality: NA == NA have value NA. For arithmetical comparisons we have
4 < NA is NA (The NA we compare to 4 might be 6, in which case we have TRUE, or it might be 2, in case it is FALSE. so we do not know, that is the value is NA).