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1) "TECHEILES" AND "LAVAN" ARE NOT "ME'AKEV" EACH OTHER

(a) (Mishnah): (The Torah commands to put woolen thread(s) dyed Techeiles on each of the four corners of a garment, in addition to Lavan (strings that are the same color as the garment, which is usually white).) Techeiles is not Me'akev the Lavan, nor is Lavan Me'akev Techeiles;
(b) The Tefilin Shel Yad is not Me'akev Shel Rosh, nor vice-versa.
(c) (Gemara) Suggestion: Our Mishnah is not like Rebbi!

1. (Beraisa - Rebbi): "U'R'isim Oso" - Techeiles and Lavan are Me'akev each other;
2. Chachamim say, they are not Me'akev each other.
3. Question: What is Rebbi's reason?
4. Answer: It says "ha'Kanaf" - strings like the corner (i.e. Lavan), and "Pesil Techeiles", and it says "U'R'isim Oso" (it refers to Techeiles and Lavan in the singular, to teach that they must both be there);

i. Chachamim explain, this connotes that you will see each of them by itself.

(d) Rejection (Rav Yehudah): The Mishnah can even be like Rebbi, it teaches that the order is not Me'akev.

1. (Beraisa): The Mitzvah is to put the Lavan first (Rashi - in each corner; Shitah Mekubetzes - the first windings (of one string around the others) should be Lavan); if one put Techeiles first, he fulfilled his obligation, but he missed a Mitzvah.
2. Question: What Mitzvah did he miss?

i. Suggestion: He missed the Mitzvah of Lavan, but fulfilled the Mitzvah of Techeiles.
ii. Rejection: This is unlike Rebbi, he says that each is Me'akev the other!

3. Answer (Rav Yehudah): He lacks a Mitzvah, and fulfilled a Mitzvah.
4. Question: What Mitzvah does he lack?
5. Answer: He did not do the Mitzvah in the best way.

(e) Question: This explains 'Techeiles is not Me'akev Lavan' - how do we explain 'Lavan is not Me'akev Techeiles'?
(f) (Shitah Mekubetzes deletes Rami bar Chama's answer from the text here, it appears later.)
(g) Levi asked similarly:

1. Question (Levi): How do you explain 'Techeiles is not Me'akev Lavan, and Lavan is not Me'akev Techeiles'?
2. Answer (Shmuel): This (the first clause) teaches about a white garment, the Mitzvah is to put the Lavan first;

i. Question: What is the reason?
ii. Answer: It says "ha'Kanaf" - strings like the corner. (Afterwards, it says "Pesil Techeiles");
iii. If Techeiles was put first, this is not Me'akev.

3. Question (Levi): This explains 'Techeiles is not Me'akev Lavan' - how do you explain 'Lavan is not Me'akev Techeiles'?

(h) Answer #1 (Rami bar Chama): This teaches about a garment that is entirely Techeiles, the Mitzvah is to put Techeiles first, for this is like "ha'Kanaf";

1. If Lavan was put first, this is not Me'akev.

(i) Objection (Rava): It does not depend on the color of the garment (we always put Lavan first)!

(a) Answer #2 (Rava): It teaches about remnants (if Tzitzis were cut off):

1. (The first clause teaches that) if the Techeiles strings were cut off and the Lavan remains, it is Kosher - (the latter clause teaches that) if the Lavan was cut off and the Techeiles remains, it is Kosher.
2. (Benei R. Chiya): Remnants of Techeiles (or Lavan strings) are Kosher; remnants of Ezov branches are Kosher (for Parah Adumah or Metzora).

(b) Question: How much must remain?
(c) Answer (Bar Hameduri): Enough must remain in order that one could make a bow.
(d) Question: Must one be able to make a bow of all the strings together, or each by itself?
(e) This question is not resolved.
(f) Question (Rav Ashi): If one could not make a bow because the strings were thick, but if they were thinner one could, what is the law?
(g) Answer (Rav Ada brei d'Rava): If they were thin, it would be Kosher - all the more so, if the strings are thicker, the Mitzvah is more recognizable!
(h) Question: Who are the Chachamim that argue with Rebbi?
(i) Answer: They hold like R. Yitzchak.

1. (Beraisa - R. Yitzchak): If one does not have Techeiles, he puts Lavan.

(j) (Rava): This teaches that one must tie the strings together after each Chulya (winding; Shitah Mekubetzes - really, we only show that it is not enough to tie after the last Chulya; Tosfos - presumably, they must be tied between each Chulya and the next);

1. If this was not necessary, if only a small remnant remains, the last knot would become undone, and the whole Gedil would become undone!

(k) Rejection: Perhaps it is not *necessary*, and Benei R. Chiya taught that remnants are Kosher only in a case in which the strings happened to be tied!