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1) TZAFTZAFAH

(a) (R. Zeira) The source for invalidating the Tzaftzafah is the Pasuk in Yechezkel (17:5).

1. The People are accused of changing from being rooted in great waters to being a Tzaftzafah.
2. This indicates that the Tzaftzafah is not water- based.

(b) Question (Abaye): Perhaps the Pasuk is only explaining what is meant by the great waters (Tzaftzafah)?
(c) Answer: The implication of Samo is that they became other (worse) than what they were (as R. Avahu read into the Pasuk).
(d) Alternate rendition of the above: The Tana cited this Pasuk to explain the exclusion of Tzaftzafah, leading to R. Zeira asking Abaye's question and R. Avahu's rendition of the Pasuk.
(e) Question: What is Aravah and what is Tzaftzafah?
(f) Answer: The stem of the Aravah is red, its leaves are long and its mouth (the outer ridge of the leaf) is smooth, unlike the Tzaftzafah.
(g) Question: But we have learned that an Aravah with ridges is Kosher!?
(h) Answer (Abaye): The Beraisa permits the sickle-edged Aravah known as Chilfa Gila.
(i) (Abaye) We may infer that Chilfa Gila is a Kosher Aravah (Hoshana).
(j) Question: Is that not obvious, given that it is an Aravah!?
(k) Answer: We might have invalidated it due to its associated name.
(l) Question: Perhaps, indeed, it is invalid?
(m) Answer: Arvei Nachal implies many types of Aravah.

(a) (R. Chisda) Three pairs of items have switched their names since the Churban, each carrying an implication in Halachah.
(b) R. Yosef added a fourth, with implication for Gittin.

3) THE NUMBER OF EACH MIN

(a) (R. Yishmael) One must take three Hadasim, two Aravos, one Lulav and one Esrog.
(b) At least one Hadas must not being Katum.
(c) (R. Tarfon) All the Hadasim may be Ketumim.
(d) (R. Akiva) Only one Hadas is required.

(a) The Beraisa provides the source for R. Yishmael's requirements, and follows with R. Tarfon's and R. Akiva's requirements regarding the Hadas.
(b) (R. Eliezer) The Esrog need not be bound together with the other three Minim, owing to the absence of the connecting Vav in the Pasuk.
(c) The absence of any of the Minim is Me'akev, as learned from Ul'kachtem.
(d) Question: On what basis does R. Yishmael only require *one* Hadas to be non-Katum (either they all must be, or none need be)!?
(e) Answer (Birah citing R. Ami): R. Yishmael retracted his requirement of three Hadasim, requiring only one, which must be whole.
(f) (R. Yehudah citing Shmuel) The Halachah follows R. Tarfon (consistent with Shmuel's threat to the Hadasim merchants against their price gouging).
(g) Question: If Shmuel wanted to follow a lenient view, why didn't he threaten to teach the Halachah like R. Akiva (requiring only one Hadas)?
(h) Answer: It is easier to find three cut Hadasim than one whole one.

(a) The Pesulim include an Esrog which is stolen, dried out, from an Asheirah and Ir HaNidachas, from Terumah Temeiah (but Terumah Tehorah, while it should not be used, is Kosher).
(b) An Esrog of Demai is a Machlokes whether it may (Beis Hillel) or may not (Beis Shamai) be used.
(c) Ma'aser Sheni in Yerushalayim while it should not be used, is Kosher.
(d) An Esrog is Pasul if most of the face of the Esrog developed s type of bubbling called Chazazis, or if its Pitom or peel came off, if it developed a crack or is missing any part.
(e) If the Chazazis only covers a minority of the Esrog, or the Oketz came off, or it has a whole without anything missing it is Kosher.
(f) A black Esrog is Pasul.
(g) A green (like Karsi) Esrog is a Machlokes whether it is Kosher (R. Meir) or not (R. Yehudah).
(h) The minimum size of an Esrog is a Machlokes R. Meir (like a nut) and R. Yehudah (like an egg).
(i) The maximum size is a machlokes R. Yehudah (must be able to hold two such Esrogim in one hand) and R. Yosi (even so large as to need to hands to hold it).