Question: Rav Nachman taught that if Bnei Mirpeses [they live in an upper story. They have a balcony with a ladder, through which they descend to the Chatzer and from there to Reshus ha'Rabim] forgot to be Me'arev with the Bnei Chatzer, they forbid only if there is no Dakah four Tefachim [tall - Rashi; Rambam - four wide and 10 tall], in front of the ladder]!

Answer: The case is, the Mirpeses is not 10 tall.

Question: If so, why does a Dakah permit? (This is like two Chatzeros without a wall between them!)

Answer: The case is, a Mechitzah surrounds the entire Mirpeses, except for 10 Amos. The Dakah shows that they withdraw from the Chatzer.

(Rav Yehudah citing Shmuel): If ladders were erected next to each other against a wall, even if the total width is more than 10 Amos, it is still considered a wall.

Question (Rav Berona): Shmuel does not hold that a ladder is a Mechitzah!

(Rav Nachman citing Shmuel): If Bnei Mirpeses forgot to be Me'arev with the Bnei Chatzer, they forbid only if there is no Dakah four Tefachim in front [of the ladder].

Answer: He discusses a Mirpeses less than 10 tall.

Question: If so, why does a Dakah permit?

Answer: The case is, a Mechitzah surrounds the entire Mirpeses, except for 10 Amos. The Dakah shows that they withdraw from the Chatzer.

People of a certain [public city that became an individual's] city asked Rav Yosef to send someone to be Me'arev their city. He told Abaye 'go be Me'arev in a way that will not arouse complaints.'

Abaye saw houses that were open to a river [and not to the city]. He decided that they will be the remnant.

Retraction (Abaye): The Mishnah says that we may not be Me'arev all of it. This implies that [if not for the decree] one could be Me'arev the remnant with it! (Therefore, these houses cannot be the remnant.)

Abaye decided to make windows [in the wall between these houses and the city], so that they could choose to be Me'arev with the city. Then, they would be a Kosher remnant.

Retraction (Abaye): This is not necessary. Rabah bar Avuha was Me'arev all of Mechuza, each neighborhood by itself, for they were separated by ditches in which date pits were stored for animals;

Each neighborhood was a remnant for the others, even though they could not Me'arev together!

Retraction (Abaye): I cannot learn from there. In Mechuza, they could have been Me'arev together through the roofs. Here, they could not, so windows are required.

Retraction (Abaye): Windows are not required. A certain man in Pumbadisa had a storage area for straw, and Chachamim made it the remnant for the city (Tosfos - together with three Chatzeros, like R. Shimon. Rashi, according to Sefas Emes - since Abaye inferred that we do not require that even part of the remnant could be Me'arev with the city, we must say that the Chatzeros were in the storage area.)

Abaye: This is why Rav Yosef warned me to be careful!

(Mishnah): We must leave a remnant as big as the city 'Chadashah'.

(Beraisa - R. Yehudah): There was a city in Yehudah called 'Chadashah'. It had 50 residents, including men, women and children. Chachamim made this the standard remnant.

Question: If one was Me'arev Chadashah, does it require a remnant?

Objection: This is obvious! Just like it is a remnant for the big city (they were not Me'arev together), the big city is a remnant for it!

Correction: Rather, if we are Me'arev a city the size of Chadashah, does it require a remnant?

(Rav Huna or Rav Yehudah): It requires a remnant.

(The other of Rav Huna and Rav Yehudah): It does not require a remnant.

(Mishnah - R. Shimon): One must leave over three Chatzeros, each with at least two houses.

(R. Chama bar Gurya): The Halachah follows R. Shimon.

(R. Yitzchak): Even one house and one Chatzer suffice.

Objection: This cannot be! (We require three Chatzeros.)

Correction: Rather, it suffices if one house opens to each Chatzer.

Question (Abaye): Did R. Yitzchak have a tradition for this, or is this his reasoning?

Rav Yosef: What difference does it make?

Abaye: Is learning merely a song [that one recites for pleasure, and need not understand all the words]?

(Mishnah): If Reuven was in the east and told his son to be Me'arev for him in the west, or vice-versa:

If he is within 2000 Amos of his house and more than 2000 Amos from his Eruv, he is permitted to [go to] house and forbidden to [go to] his Eruv;

If he is within 2000 Amos of his Eruv and more than 2000 Amos from his house, he is permitted to his Eruv and forbidden to his house. (This will be explained.)

If one put an Eruv in the Ibur of the city, it has no effect.

If one put an Eruv outside the Techum, even one Amah outside, whatever he gains [in that direction] he loses [in the opposite direction].

(Gemara) Assumption: The Mishnah means [that Reuven was] to the east of his house [and told his son to be Me'arev in the west], or [vice-versa, i.e. Reuven was] to the west of his house [and told his son to be Me'arev in the east].

Question: We understand how he can be within 2000 of his house and more than 2000 from his Eruv, i.e. when he walks 2000 Amos [west], he reaches his house but does not reach his Eruv;

However, how can he be within 2000 Amos of his Eruv and more than 2000 Amos from his house?

Answer #1 (R. Yitzchak): Your assumption is wrong. The Mishnah discusses [Reuven being] east of his son and [in the vice-versa case] west of his son.

Answer #2 (Rava bar Rav Shila): Really, it refers to east and west of his house. The case is, his house is on a diagonal (like the diagram in Rashi, illustrating the vice-versa case. He is southwest of his house, and due west of his Eruv. His Eruv is [far to the south and just a bit] east of his house).

(Mishnah): If one put an Eruv in the Ibur...[if it is outside the Techum...]

Objection: Surely, it is not outside the Techum! (Such an Eruv is invalid.)

Correction: Rather, it means if it is outside the Ibur.

(Mishnah): Whatever he gains he loses.

Question: He loses more than he gains!

(Beraisa): If one put an Eruv in the Ibur of the city, it has no effect;

If he put it outside the Ibur [e.g. to the east], even one Amah outside, he gains that Amah [to the east], but [to the west] he loses [it and the width of] the entire city. [Beforehand, the entire city counted like only four Amos. Now,] its true measure is deducted from the 2000 Amos that he may go [to the west].

Answer: The Mishnah discusses when his 2000 Amos extend pass the city. The Beraisa discusses when his 2000 Amos end in the city:

(R. Idi citing R. Yehoshua ben Levi): If Reuven [lodged outside a city, and] counted his steps and found that his 2000 Amos end in the middle of the city, he may go only up to there;

If his 2000 Amos contain the end of the city, the entire city counts like only four Amos, and he counts the rest of his 2000 Amos past the city.

Objection (R. Idi): These are like words of prophecy [without rational explanation]! What is the difference whether his 2000 Amos extend pass the city, or end in the city?!