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- Bemare Habazak - Rabbis Questions
Answer: According to your description, the tzitzit are kosher without reattachment, as we will explain. If the other tzitzit are of kosher length (details are not our focus) and only one string ripped, the tzitzit remain kosher for the following reason. The Shulchan Aruch (Orach Chayim 12:1) cites two opinions on leeway regarding ripped tzitzit strings. The Ri posits that each of the four strings can be "too short" on one of its ends if the other end is the proper length. (Background – each corner of the tzitzit has four strings, which look like eight because both ends of the strings face in one direction. One can know the pairings of the string ends if he, as recommended, was consistent about keeping the same four string ends together on opposite sides of the knots.) Rabbeinu Tam holds that two of the four strings must be complete on both ends. If only one of the eight strings became too short, the tzitzit are kosher according to all.
Bemare Habazak - Rabbis Questions (654)
Rabbi Daniel Mann
571 - Peeling an Egg with Writing on it on Shabbat
572 - Reattaching Ripped Tzitzit
573 - Moral Culpability for Unintentional Actions on Shabbat
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The Taz, though, points out that the connection needs to be made at the right time, because of the concept of ta’aseh v’lo min he’asuy (=tvlmh). This means that regarding mitzvot that require acting to create the object of the mitzva (including sukka or tzitzit), the creating must be significant at the time it was done, as opposed to receiving its significance retroactively. For example, if one tied three sets of tzitzit strings on a three cornered garment (for which there is no mitzva of tzitzit) and later forms a fourth corner, the existing sets of strings are invalid until he redoes them (Shulchan Aruch. OC 10:5). So, says the Taz, if one tied strings together before attaching the tzitzit to the garment, all is fine. However, if one originally attached tzitzit strings that were too short and tied on extensions afterwards, it is pasul because of tvlmh.
What is more complicated is when the tzitzit were fine when they were attached, later strings ripped, and one wants to return them by tying. This seems to depend on a difference of opinion regarding a case of a mitzva that was done properly, lost relevance, and was restored (see Pitchei Teshuva, Yoreh Deah 286:13, regarding mezuzot on a doorway which went in, out, and back into obligation in mezuza). The Ba’er Heitev (OC 12:3) cites our Taz as saying that our case would be fine, but the Sha’arei Teshuva (ad loc.), Eliya Rabba (12:1), and Mishna Berura (12:7) point out that the correct reading of the Taz is that it is pasul.
However, the Mishna Berura (ibid.) points out that if one fixed a string when the tzitzit had enough kosher strings, it is not a problem of tvlmh, and the string apparently counts in your case. The value of fixing can show itself if other strings rip even later. Also, an individual short string is not optimal (see Taz ibid.), and reattaching the string apparently fixes that drawback.

Kuzari -Rabbi Ari Shvat Kuzari class 8- "Answering Questions on the Kuzari's Proof from Mass Revelation
Lessons
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Kuzari -Rabbi Ari Shvat Kuzari class 9 - "Seeing is Believing" (parag. 21-30)
These paragraphs elaborate on the theme that seeing and knowing is better than any attempt to prove logically, and begins explaining the difference between Israel and gentiles.

Ein Aya Various Universal Stages of the Geula Process
Rav Kook examines the various stages of redemption, explaining how (in addition to the obvious oft-mentioned stages of ingathering the exiles, reviving the Hebrew language, army, state etc.) the messianic dream of world prosperity, the State of Israel and world unity can and are realistically and logically gradually coming true.

Kuzari -Rabbi Ari Shvat Kuzari class 8- "Answering Questions on the Kuzari's Proof from Mass Revelation
How do we know that the "claim" of mass revelation to 2,000,000 witnesses at Mt. Sinai is really true? This important class answers all of the questions skeptics ask about this claim of the Kuzari.

Ein Aya Armies Still Necessary for Balance & the War Against Wars
Rav Kook explains why the world was originally divided into the various seemingly contradicting ideologies and cultures, in order to develop each one respectively. Swords or armies symbolize how each respective ideology defends themselves, as well as deters their opposing ideologies and cultures. On the other hand, the messianic era will be one of peace, and Rav Kook explains the transition to that stage, which mankind is already undergoing.

The Land of Israel LGBT'S IN ISRAEL
The question was asked, how can one make Aliyah with the LGBT parades?

Kuzari -Rabbi Ari Shvat Kuzari class 7 - Five Accumulative Proofs of G-d
As a preparation for the Kuzari's classic proof of G-d from the mass-revelation at Sinai, we start here with 5 other directions to strengthen our belief which also contribute to what the Kuzari will present as well.

Ein Aya Muscle & Meaning: The Dual Nature of Gevurah (Physical Strength)
Is physical strength and fitness a necessity or an ideal? Although it if often totally overlooked among topics of Judaism, Rav Kook writes that it clearly is also a necessity to deter the many enemies of Israel, but even in Y'mot HaMashiach, in the Messianic era, to a certain extent, it's ideal continues even after our enemies will have been finished off.








