What are you supposed to do if you inadvertently broke your fast*? Do you:
- keep going;
- extend it (if so, how long);
- cancel it (if so, do you make it up a different day)?
*This question is for day-fasts only.
The Mishna Brura OC 549 sk 3 says to continue fasting if you accidentally ate.
In OC 568 sk 3 he says you can still say Aneinu at Mincha if it is a public fast day (as opposed to a personal one).
In OC 568 sk 8 he says that you do not need to fast again on a different day for accidental eating on the public fasts as well as any personal fast that has a fixed date (eg Yahrtzeit).
This halacha is not limited to Yom Kippur and Tish'a b'Av, but applies to "minor" fasts, as well.