1)

(a)Our Mishnah discusses the threads of the Tzitzis - two of which must be dyed Techeiles.

(b)One has to have four (double) threads in any case. Neither is the white Me'akev the Techeiles, nor is the Techeiles Me'akev the white (See also Tosfos DH 'ha'Techeiles').

(c)The shel Yad and the shel Rosh - are not Me'akev each other either.

2)

(a)We suggest that our Mishnah does not go like Rebbi in a Beraisa, who learns from the words "al Tzitzis ha'Kanaf" (in the Pasuk in Sh'lach l'cha "Venasnu al Tzitzis ha'Kana P'sil Techeiles") that - the Tzitzis must be of the same color wool as the (corner of the) garment ...

(b)... which means that they must be made of white threads - since most garments in former times were made of white linen.

(c)And he then learns from ...

1. ...the fact that the Pasuk adds "P'sil Techeiles" - that the garment also requires Techeiles (dark-blue woolen) threads.

2. ... "u'Re'isem Oso" that - the two are Me'akev each other.

(d)The Rabbanan counter that - by pointing to the word "Oso" - (singular), that they are not Me'akev each other, and someone who possesses only one of them is Yotzei.

3)

(a)To reconcile our Mishnah with Rebbi, Rav Yehudah Amar Rav, based on a Beraisa, explains Me'akeves in our Mishnah - with regard to the order of precedence (that the order of tying them is not Me'akev, in that Bedi'eved, even if one first ties the Techeiles threads one has nevertheless fulfilled the Mitzvah ...

(b)nevertheless, Lechatchilah one should tie the Lavan first - because Lavan is written first in the Pasuk.

(c)When the Beraisa concludes ve'Im Hikdim Techeiles le'Lavan Yatza, Ela she'Chisar Mitzvah, the Tana cannot mean that he is lacking the Mitzvah of Lavan - because then he would not be Yotzei at all according to Rebbi.

(d)Rav Yehudah Amar Rav therefore explains it to mean that - although he has performed the Mitzvah of Lavan and Techeiles, he is lacking the Mitzvah of giving the Lavan precedence.

4)

(a)We just explained how Lavan is not Me'akev Techeiles, even according to Rebbi. Rami bar Chama explains our MIshnah ('ha'Techeiles Einah Me'akeves es ha'Lavan') according to Rebbi - by establishing the case by a garment that is made of Techeiles (so that Miyn Kanaf refers to Techeiles, with which one ought therefore to have started tying the threads [but didn't]) ...

(b)... and that is also how he ultimately explains Sh'muel's explanation of ha'Techeiles Einah Me'akeves es ha'Lavan.

(c)Shmuel was called Aryoch, which means 'king - because in money matters the Halachah is always like him (like a king, about whom Chazal have said Diyna de'Malchusa Diyna).

5)

(a)Objecting to Rami bar Chama's explanation, Rava claims Midi Tziv'a ka'Garim, by which he means that - it is not the color of the garment that determines Miyn ha'Kanaf ...

(b)... but after the majority of garments, which, as we explained - tends to be made of white linen. Consequently, one is always obligated to begin with Lavan and not with Techeiles.

(c)So he interprets ha'Techeiles Einah Me'akeves es ha'Lavan, ve'ha'Lavan Eino Me'akev es ha'Techeiles in our Mishnah - with regard to Gardumin - what remains after the Tzitzis tear), even according to Rebbi.

(d)He therefore explains the Mishnah (ha'Techeiles Einah Me'akeves ... ) to mean that- whether the Lavan threads tear and the Techeiles remains, or vice-versa, the Tzitzis are Kasher, because one is not Me'akev the other.

6)

(a)Rava's explanation is based on the ruling of b'nei Rebbi Chiya, which we discussed in the previous Perek (regarding Gardumei Techeiles and Gardumei Eizov). bar Hamduri quoting Shmuel gave as the Shi'ur of Gardumei Techeiles - sufficient thread to tie into a single knot.

(b)The two possible interpretations of K'dei le'Anvan that the Gemara present are - either enough to tie all the remaining threads together into a knot, or enough to tie each thread independently.

(c)We do not know which is the correct one - because the She'eilah remains unanswered.

7)

(a)Rav Ashi asked what the Din will be in a case where the threads are too thick to tie into a knot -though it would be possible to do so if the same threads were of a regular thickness. He asked whether that is considered K'dei Le'anvan' (and is therefore Kasher), or nor.

(b)Rav Acha b'rei de'Rava resolved Rav Ashi's She'eilah - by pointing out that there where thin Tzitzis would be Kasher, thick ones certainly are, seeing as they possess the advantage of being more discernible.

8)

(a)The Tana who argues with Rebbi is Rebbi Yitzchak ... in the name of Rebbi Yochanan ben Nuri, who says that - someone who has no Techeiles - should use Lavan instead.

9)

(a)Bearing in mind that Rava disagrees with the previous presumption that Gardumei Techeiles must require a Shi'ur (see Tosfos DH 'K'dei Le'anvan'), his basis for saying that each Chulya (group of rings) requires a knot is - because otherwise, how could the b'nei Rebbi Chiya declare Girdumei Techeiles Kasher, seeing as, once the Tzitzis tear right down to the top knot, it is bound to come undone. Now if there were no more knots except for the one by the Kanaf, all that would then remain would be threads (P'sil) without the encircled part (the G'dil), which would be Pasul.

(b)We refute Rava's proof however - by establishing the b'nei Rebbi Chiya where the owner opted to tie knots for each Chulya (but not because it was a Mitzvah to do so).

10)

(a)We learn from the juxtaposition (Semuchin) of the Pesukim in Ki Seitzei "Lo Silbash Sha'atnez" and "Gedilim Ta'aseh lach" that - the Mitzvah of Tzitzis (tying Tzitzis [incorporating Techeiles]) on a garment of linen [Sadin be'Tzitzis]) overrides the Isur of Kil'ayim.

(b)Rabah (or Rava) proves from there that the top (double) knot must be d'Oraysa - because if it was not, why would we require a Pasuk to permit Sadin be'Tzitzis, seeing as without the knot, one only sticks the Tzitzis into the garment once (and 'Tekifah Achas' is not considered joined), in which case there is no Isur Sha'atnez to begin with.

(c)Despite the fact that it really makes no difference where one ties the knot, Rabah refers specifically to Kesher Elyon - because if one were to tie only one knot, that is where one would logically tie it, in order to retain the G'dil.

(d)We need a proof that Kesher Elyon d'Oraysa, because, even though without it, the G'dil will not hold permanently - it might hold for a day or two if one arranges the rings tightly (particularly if one adds a single knot).

11)

(a)Some take Kesher Elyon to mean specifically the knot next to the garment. And the reason that Rabah refers specifically to that knot and not to the knot at the end of the Tzitzis is - because the latter is too far from the place were the Tzitzis joins the garment to constitute Sha'atnez.