Opinion: An incident came before Rabeinu Tam where it was rumored that a certain Get was invalid, and therefore a second Get was given due to this rumor. Rabeinu Tam did not require the woman to wait three months from the time of the second Get, being that the first Get was in fact valid. The second Get was only due to the suspicion of the rumors.

Proof: He proved this from our Gemara. We say here that she is permitted to both of them, even though it is akin to remarrying his wife who he had divorced from Eirusin (and whom another man had married in the interim). Being that this is all only based on rumor, they were not stringent (that she should not marry her first "husband").

Question: The Ri says that there is no proof from our Gemara. Our case is different, as there are rumors from both husbands, and it is therefore not so comparable to a case of a person remarrying his wife whom he had divorced from Eirusin. However, we should be stringent when the rumor is different (Tosfos Rosh - when there is only one rumor), as stated earlier that when it was not made clear that the rumor was true, she should not get divorced from the second husband and marry the first. This is despite the fact that the first Kidushin is only an unverified rumor. Even so, we are stringent due to the second husband's Kidushin that clearly was valid according to Torah law. It is more comparable to remarrying one's wife from Eirusin.

Opinion#1: Rashi explained that "Ki Savo," "Ki Yivee'acha," and "Ki Va Sus Pharoh" all mean "d'Ha" -- "that." It cannot be that it is in place of "Im" -- "if," as Hash-m certainly brought them to Eretz Yisrael, and certainly made Pharoh's horse come to the Yam Suf.

Opinion#2: Rabeinu Tam understands that Rashi did not have to give this explanation, as we often find the word "Im" (normally translated as "if") used in this way. For example, the Pasuk says, "Im Takriv Minchas Bikurim," "Im Kesef Talveh," "Ad Im Keelu Lishtos," and "Im Yihyeh ha'Yovel l'Vnei Yisrael"

Observation: The Yerushalmi asks, why is the Pasuk, "Her husband who sent (i.e. divorced) her cannot return to marry her" necessary? We should understand that this is forbidden from the fact that a person cannot remarry his former wife who was a Sotah being that there are witnesses. The Yerushalmi answers that it is in order for there to be two negative prohibitions against this.

Text: Some Sefarim have the text, "Beis Hillel and Beis Shamai."

Opinion#1: The Ri says that Rebbi Akiva holds like Beis Shamai who says that "Ervas Davar" is one thing. If they are two different things, "Ervah" or "Davar," why say "Davar" when referring to her burning his cooked dish once the Pasuk, "If she will not find favor in his eyes" permits divorce if he found a more beautiful woman?

The word "Ervas" teaches that she can marry someone else after she gets divorced (even if it is due to promiscuity), and certainly this is the case if she was divorced because she burned his food.

Accordingly, it is understandable why the Sefarim's text is "And Beis Shamai" and not "And Beis Hillel." This teaches us that even though Rebbi Akiva and Beis Shamai agree regarding their understanding of "Ervas Davar," they still argue regarding whether or not one can divorce a woman if he finds a prettier woman (dependent on how one understands the word "Ki" as explained in the Gemara).

Opinion#2: Rebbi Elchanan explains that Rebbi Akiva can agree with Beis Hillel. If the word "Davar" was not extra to tell us that he can divorce her if she burned his food, he would not have derived that the word "Ki (Matza Bah)" means "(also) if."

Explanation#1: Rashi explains that if so, there is circumstancial evidence that she is a Zonah and is therefore forbidden to him. It is an obligation to divorce her, not just a Mitzvah!

Question: A woman who knits in the marketplace and she goes out with her head uncovered also must be divorced. It is not merely a Mitzvah to divorce her. The Gemara in Sotah (25a) asks whether or not it is permitted to continue being married to a woman who transgress Das Yehudis (the Rabbinic code of modesty), and the Gemara does not answer the question. Why, then, doesn't our Gemara ask regarding these types of women (that it mentions in the same sentence) that it must be an obligation to divorce her?

Answer: Being that the question in Sotah is only a Rabbinic question, it is understandable why it only said that it is a Mitzvah to divorce her. However, it is a Mitzvah according to Torah law to divorce this woman.

Explanation#2: It is also possible to explain that the Gemara was asking, "Is it possible that it means she was bathing with men? Even a bad person does not allow his wife to bathe with men, and even a loose woman does not do this!"

Explanation: This is even according to Beis Hillel, and is referring to the part of the Pasuk that says the divorce was due to "Ervas" -- "promiscuity."