the various meanings of ‘counterexample’

1. an instance contradicting a purposed general proposition; Wikipedia has an entry on this notion. Here it is.
2. an example showing that omission of a certain part of the hypothesis of a certain theorem results in a statement that is not a theorem; Wikipedia is fond of this usage. Here is the link to an example of such.
3. a non-fatal anomaly left unaddressed by a stylized fact; Wikipedia has an entry on the notion of ‘stylized fact’. Here it is.
keywords: Logic, Mathematics, terminology, wide-sense, narrow-sense