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Is there any prohibition to remove a disconnected beard hair from a beard on Shabbat? In order to remove the hair you still may have to move away other parts of the beard to get to the hair in question.
At first I thought that this might be Borrer (that is, the melacha (forbidden 'labor') of selection), but I'm not too sure that we could call connected hair and disconnected hair a taarovet (mixture)... or could we?
Also, any problems other than borrer?
I'd say there's no problem because you can't pick the connected hair. Borrer is when you pick the Psolet (or what you don't want) out of the food (what you do want). It's like picking a shoe that happens to be in the middle of a row of other shoes that are nailed to the floor.
A more Talmudic could-be-proof, is from Mishna Beitza 23a:
רבי יהודה אומר אין מקרדין את הבהמה ביום טוב מפני שעושה חבורה אבל מקרצפין וחכמים אומרים אין מקרדין אף לא מקרצפין
Translation (self-made):
R' Yehuda says: it's forbidden to Lekared the beast in Yom Tov since it bruises (the beast) but it's allowed to Lekartzef. Chachamim say: both are forbidden.
And the Talmud on that Mishna explains what's Lekared and Lekartzef and the reasoning of the different opinions:
תנו רבנן איזהו קרוד ואיזהו קרצוף קרוד קטנים ועושין חבורה קרצוף גדולים ואין עושין חבורה וג' מחלוקות בדבר רבי יהודה סבר דבר שאינו מתכוין אסור מיהו קרוד קטנים ועושין חבורה קרצוף גדולים ואין עושין חבורה ולא גזרינן קרצוף אטו קרוד ורבנן סברי נמי כר' יהודה דבר שאינו מתכוין אסור וגזרינן קרצוף אטו קרוד ור' אלעזר בן עזריה סבר לה כר' שמעון דאמר דבר שאינו מתכוין מותר ובין קרוד ובין קרצוף שרי
Translation (again self-made):
Tanu Rabanan: what is Kerud and what is Kirtzuf? Kerud - little and bruises (Rashi - combing with an iron comb that has thin teeth), Kirtzuf - big and doesn't bruise (Rashi - combing with a wooden comb that has thick teeth), and three opinions are involved in the disagreement: R' Yehuda thinks that davar she'eino mitkaven is forbidden, however that applies to Kerud that has thin teeth and bruises and not to Kirtzuf that has thick teeth and doesn't bruise, and R' Yehuda doesn't decree to prohibit Kirtzuf just because Kerud is forbidden. Rabanan agree with R' Yehuda that davar she'eino mitkaven is forbidden but they do decree Kirtzuf because of Kerud so they forbid both. And R' Elazar Ben Azaria thinks like R' Shimon that said that davar she'eino mitkaven is allowed, thus he allows both Kirtzuf and Kerud.
Since the only thing that apparantly bothers the Tanaim is making a Chabura (bruise) (and the Tosfot also mention Isur Tolesh - tearing of hair), it seems that Borrer isn't a problem. My preassumption here, though, is that this also applies to Shabbat as it applies to Yom Tov (don't have a proof for that yet).
