The Mechaber writes that the optimal time to count sefira is after tzeis hakochavim - the appearance of the stars-- but if one counts earlier, during the period known as bein hashemashos, he has fulfilled his obligation. The Mishnah Berurah cites poskim who hold that one who counted before tzeis should count again after tzeis without a beracha. This is because sefira nowadays is still considered m'doraisa by some Rishonim, and a mitzvah doraisa that is to be performed at night needs to be done after tzeis since it is questionable whether bein hashemashos is night.
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Hilchos Tzitzis 13 (page 49)
When Kavod Habriyos Overrides an Issur
Torn Tzitzis on Shabbos
Torn Tzitzis During the Week
When kavod habrios overrides an issur
The Gemara says: "Great is kavod habriyos, for it overrides a Torah prohibition." This means that there are circumstances in which a person is exempt from fulfilling a mitzva or permitted to violate an issur if fulfilling the mitzva or refraining from the issur would cause him embarrassment. A situation that could cause a terrible embarrassment can justify violating a d'oraisa in a passive manner (shev v'al ta'ase), and a situation that could cause lesser embarrassment can justify overriding a d'rabonon in an active manner (kum v'ase). The severity of the embarrassment is judged by the people involved. A situation may be considered an embarrassment to one person but not to another.
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Torn tzitzis on shabbos
A talis whose tzitzis tore on Shabbos can be worn as is, since the strings cannot be replaced on Shabbos. If the strings came off in public in a karmelis and removing the talis would embarrass the wearer, it does not need to be removed. The Rabbinic prohibition of carrying the talis in a karmelis is waived to prevent embarrassing the wearer. The poskim discuss whether this rule is limited to a talis koton or whether it can be applied to a talis gadol as well. If the incident occurred in a reshus harabim where carrying is forbidden mid'oraisa, the garment may not continue to be worn, since doing so constitutes a kum v'ase.
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Torn tzitzis during the week
If the tzitzis ripped from a talis on a weekday, it is forbidden mid'oraisa to wear it. Every moment it is worn is a violation of the commandment to put tzitzis on one's garments. If the tzitzis ripped from a talis koton in a public area where it is embarrassing to remove it, the wearer must go immediately to a private place where the talis can be removed. Although it involves an issur d'oraisa, the wearer does not need to remove it in public since it is a passive violation (i.e. not putting on the strings). If a talis gadol ripped, it must be removed immediately since not wearing a talis gadol does not entail a great embarrassment. The poskim discuss whether removing a talis gadol in shul during davening is considered a 'terrible embarrassment.' If this situation occurs, it is wise to be mafkir the talis since an ownerless garment does not require tzitzis.
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On Shabbos it is permissible to wear a talis gadol or talis koton in a reshus harabim. The strings are not considered a 'forbidden load' but rather as a necessary component and an adornment to the garment.
A garment that has some tzitzis but lacks the proper amount (some strings were never put on) may not be worn in a reshus harabim or a karmelis because in such a case, the few 'kosher' strings are not considered part of the garment.
According to some poskim, a garment which is smaller than the necessary shiur and has tzitzis may not be worn in a reshus harabim or karmelis on Shabbos, while other poskim permit wearing it.