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Wearing Tzitzis on Shabbos: 
On Shabbos, it is Biblically permitted to wear a four cornered garment without Tzitzis. However Rabbinically, it is forbidden to do so. [Furthermore, one who wears a four cornered garment with Tzitzis fulfills the Biblical Mitzvah even on Shabbos.]
A Shabbos Tallis: One who is able to afford a second Tallis should have a second Tallis specifically designated for wearing on Shabbos.
Checking the Tzitzis on Shabbos: See Chapter 2 Halacha 5!
Carrying: A Tallis Gadol or Katan that contains Kosher Tzitzis may be worn in a Reshus Harabim. This applies whether during the day or at night. One however must beware not to walk in a Reshus Harabim with the Tallis on one’s shoulder, in a way that is not normally worn during the week.
Invalid Tzitzis: It is Biblically forbidden to wear a Tallis that contains invalid Tzitzis that are still useable, within a Reshus Harabim, and one who does so is liable for a sin offering. This includes the following cases: If one only tied Tzitzis to three of the corners, it is Biblically forbidden to wear such Tzitzis in a Reshus Harabim. Likewise, if all four Tzitzis have been tied to the corners and an invalidation occurred in one of the Tzitzis, then even if an invalidation occurred in all four corners of Tzitzis due to tears of strings to a length shorter than Kdei Aniva, nevertheless he may not wear these Tzitzis in a Reshus Harabim. If however all the strings of all the four corners have torn in an invalidating manner and there is not even one string remaining that is of the valid measurement that can be salvaged for use for future Tzitzis, and one must hence remove all four corners of Tzitzis and tie new ones to the corners, then the Tallis with these torn strings is not forbidden to wear in a Reshus Harabim due to the carrying prohibition. It is however forbidden to wear it due to the prohibition against wearing a four cornered garment without Kosher Tzitzis. If however the Tallis is borrowed, and is thus not obligated in Tzitzis, then one may wear it.
Checking the Tzitzis prior to walking in an area without an Eiruv: One is not required to check his Tzitzis, to verify its Kashrus status, prior to walking through a Reshus Harabim, so long as the Tzitzis were already checked that day.
May one wear on Shabbos an invalid Tallis that has Kosher Tzitzis in an area without an Eiruv?
- Example-The sides of the Tallis are majority sewed, hence exempting it from Tzitzis; or the Tallis Katan is smaller than 1×1 Ama and is hence exempt from Tzitzis.
What is the law if Tzitzis was made on Shabbos?
If it was done Beshogeg the Tzitzis are Kosher. If however it was done Bemeizid, then the Kashrus of the Tzitzis is questionable.
May one wear a four cornered garment without Kosher Tzitzis if he does not have any Tzitzis available?
Some Poskim rule that if there are no Tzitzis available in the city, there is no Biblical prohibition involved in wearing a four cornered garment without Tzitzis. Nevertheless, it is Rabbinically forbidden to do so. Other Poskim however rule it is Biblically forbidden to wear a Tallis even in such a case. The practical ramification is regarding a case that one found an invalidation on his Tallis, as explained in Chapter 4 Halacha 15.
 Admur 13/7; Taz 13/5; M”A 13/8
 The reason: As the positive command to place fringes on the garment only begins after one initially wears the four cornered garment, as the Torah does not state “Don’t wear a garment without Tzitzis”. Now, on Shabbos, since it is forbidden to tie Tzitzis to a garment due to the Shabbos prohibition, therefore one cannot fulfill this command. [Admur ibid; Taz ibid] Hence, one must conclude that the Torah does not prohibit one from wearing a non-fringed four cornered garment on Shabbos.
 Admur ibid; M”A 13/8
The reason: As by wearing the four cornered garment without Tzitzis one is actively causing himself to nullify the positive command of tying Tzitzis. [Admur ibid] Seemingly, this means to say that since even on Shabbos one fulfills the positive command by wearing a four cornered garment with Tzitzis, therefore by entering oneself into a situation that he will be unable to place the Tzitzis on the garment he is actively causing the positive command to be nullified.
Other opinions: Some Poskim rule there is no Rabbinical prohibition to wear a four cornered garment without Tzitzis on Shabbos. [Mordechai brought in Beis Yosef, and P”M 317 M”Z 5; Olas Tamid brought in M”A ibid]
 Seemingly, although on Shabbos there is no Biblical prohibition to wear a four cornered fringeless garment, nevertheless, one who does wear a four cornered garment with Tzitzis, [such as it was fringed prior to Shabbos], has fulfilled a Biblical Mitzvah. Meaning, although there is no Biblical prohibition to wear a fringeless four cornered garment, one who does so has fulfilled a positive command. This is implied from the wording of Admur that Rabbinically on Shabbos one may not wear a four cornered fringeless garment “due to that he will be lead to nullify a positive command”, being that he is restrained from placing the fringes on the garment. This implies that the positive command applies even on Shabbos and it is just that there is no Biblical prohibition involved if one does not keep it. This is unlike the ruling regarding Tzitzis at night, in which case there is no Mitzvah at all to wear Tzitzis during the night.
 Admur 262/3; M”A 262/2; M”B 262/5
 13/2; Michaber 13/2
Other opinions: The Brisker Rabbis were accustomed not to wear a Tallis Gadol or Katan on Shabbos in a Reshus Harabim, due to the carrying prohibition, that in their opinion applies to Tzitzis that does not have Techeiles strings. [See Teshuvos Vehanhagos 4/4; Piskeiy Teshuvos 13 footnote 4]
 The reason: As Kosher Tzitzis is considered an ornament and accessory of the Tallis, just as is the rim of a garment and its other parts. Therefore, the Tzitzis are not considered like a package being carried. [ibid] This applies even today when Techeiles is no longer found [Admur ibid; Michaber ibid] and we are thus unable to properly fulfill the Mitzvah of Tzitzis with two Techeiles strings.
 Admur ibid; M”A 13/1; Taz 18/1; Beis Yosef 13; Radbaz 1/244; Kneses Hagedola 13/4; Olas Tamid 13/3-4
The reason: Although nighttime is not a time of Tzitzis, nevertheless it is permitted being that Kosher Tzitzis is considered an ornament and accessory of the Tallis, just as is the rim of a garment and its other parts. [Admur ibid]
Other opinions: Some Poskim rule it is forbidden to wear Tzitzis on the night of Shabbos in an area that does not have an Eiruv. [opinion in Kneses Hagedola 13; Birkeiy Yosef 13/2]
 Admur ibid; Rama 13/2; As explained in Admur 301/35
 13/1; Michaber 13/1
 The reason: The reason for this is because when the Tzitzis are invalid they do not contain a Mitzvah and are hence considered like a package that one is carrying. Now, although they are attached to the Tallis, nevertheless they are not nullified to the Tallis being that the strings are important in his eyes, as he plans on still using them to make Kosher Tzitzis. For this reason, the un-torn strings are not nullified to the Tallis and are considered like a package being that they are now invalid and are not an ornament or accessory for the Tallis, as the Tallis does not need these strings at all. [Admur 13/1]
 The reason: In the event that one only tied Tzitzis to three of the corners the Tzitzis these three Tzitzis are considered a “package” being that they important in his eyes, as he plans to keep them until he ties the fourth Tzitzis. For this reason, these strings are not nullified to the Tallis and are considered like a package being that they are now invalid and are not an ornament or accessory for the Tallis, as the Tallis does not need these strings at all. [Admur 13/1]
 The reason: If a tearing invalidation occurred in all four corners of Tzitzis, it is still considered like one is carrying a package as the remaining un-torn strings are important in his eyes as they are still salvageable for use for other Tzitzis. For this reason, the un-torn strings are not nullified to the Tallis and are considered like a package being that they are now invalid and are not an ornament or accessory for the Tallis, as the Tallis does not need these strings at all. [Admur 13/1]
 The reason: As these strings have no importance to him and are hence nullified to the garment. [Admur 13/1]
 13/3; Rama 13/2
 The reason: As since the Tzitzis were already checked one time that day we establish it in accordance to its Chazaka as explained in 8/13. [ibid]
 M”B 13/1
 Toras Shabbos 301/35; Aruch Hashulchan 13/2; Ashel Avraham Butchach 16; Daas Torah 13; Meishiv Davar 1/2; Eretz Tzevi 1/1; Minchas Yitzchak 4/6; Chazon Ish 3/28; Even Yisrael 7/17; Piskeiy Teshuvos 13/1
 P”M 18 M”Z 1; Kaf Hachaim 18/3
 M”A 13/8; P”M 13 A”A 8; Chayeh Adam 11/35; M”B 13/16; Poskim in Kaf Hachaim 13/12
 The reason: As since one is Anus, it is similar to Shabbos in which we rule there is no Biblical prohibition against wearing Tallis without Tzitzis. [P”M ibid]
 P”M 12 A”A 7 based on M”A 13/8 and Admur 13/6
 Elya Raba 13/6; Mamar Mordechai 13/5; Taz 13/5
Ruling of Admur: Admur in 13/6 omits the above ruling of the M”A ibid and writes similar to the wording of the Taz which implies to negate the opinion of the M”A, and to hold stringently. However, in 12/6 Admur rules like the M”A 12/7 that one may be lenient like the Riy if he does not have other Tzitzis available and the P”M ibid explains the reason behind the M”A ibid ruling is because when one does not have Tzitzis it is only a Rabbinical prohibition, and by a Rabbinical prohibition one may be lenient.
 The reason: As the week is a time that Tzitzis can be tied and hence even if there are no Tzitzis available, one may not wear a Tallis without Tzitzis. [Elya Raba ibid]