Three (possibly distinct) examples:
- A date which never exists/existed, like February 31
- A date which was 'skipped' because of calendar changes. When Russia transitioned from the Julian to the Gregorian calendar it 'skipped' October 26, 1917, among other days.
- A date/time which was 'skipped' due to a daylight savings change, like 02:01 on 03/27/2011 in the USA
These all appear to be properly formatted, but don't exist, at least in some parts of the planet that recognize the standard US date/time lexicon.
This question discusses the phrase to show to application users when they choose an invalid date, but invalid date would include 01/blah/-2 and other entries that don't conform to an accepted date format.
I've been using the term irrational date, but I'm not a mathematician and don't know if it is appropriate to compare these situations to irrational numbers.