Observation: The questioner did not think to differentiate that a person will not mix up a wall and a document.

Explanation #1: Rashi explains that this refers to sale documents.

Explanation #2: Earlier (116b and 117b), Rashi explained that this refers to letters that are sent to appease people.

Question: I am not sure why the Gemara made a point of saying it is low (where he can reach it), as the Gemara seems to understand at this point that everyone holds of Rabah.

Explanation: This means that both will be forbidden lest he erase.

Explanation #1: According to Rashi's explanation, it must be that we establish the case as when the writing is on the wall and he cannot reach it. According to the opinion that we suspect he will erase it, it is forbidden due to the statement of Rabah. According to the opinion that he will possibly read Shtarei Hedyotos, he does not hold of Rabah.

Explanation #1 (cont.): The Gemara currently wants to say that the Tanaim's argument hinges on Rabah's statement, just as the Amoraim here argue regarding the same matter. The first Beraisa can be understood as discussing a case where he writes with ink on a wall and he cannot reach it, as all Amoraim hold that one does not confuse a wall with a document.

Question: There is a difficulty with this explanation. This means that their argument is different from how it was originally stated, that according to the opinion that we suspect he will erase we do not make a decree, while according to the opinion that one might read Shtarei Hedyotos we do make a decree (see Maginei Shlomo for an answer to this question).

Explanation #2: Rabeinu Porat explains that both Abaye and Rav Bibi do not hold of Rabah, as they argue in a case where he wrote on the wall and he cannot get to it. There is no suspicion according to the opinion that we usually suspect erasure, since it is high up and we do not hold like Rabah. This opinion also does not suspect that one might come to read Shtarei Hedyotos, as one does not confuse a document and a wall. The opinion that says we do suspect people will come to read Shtarei Hedyotos holds that people will come to read Shtarei Hedyotos if they are allowed to read walls.

Explanation #2 (cont.): Abaye does not establish the argument between Rebbi Acha and the Rabbanan as being according to Rabah, as if so Rebbi Acha would not hold of Abaye's opinion that it is permitted on a wall. This implies Abaye holds that one will not confuse a wall with Shtarei Hedyotos. If so, who does Abaye hold like? Even the Rabbanan only argue on Rebbi Acha because they hold of Rabah, and they decree that one might come to erase!

Explanation #2 (cont.): Rather, Abaye explains that everyone does not agree with Rabah, and we do not suspect he will erase in a case where it is high up. The argument is whether one will confuse a document with a wall.

Implied Question: The Gemara says that we see that Rabah's law is the subject of an argument among the Tanaim. It could have said that everyone does not hold of Rabah's law, as is indeed the opinion of Abaye. (Why didn't it say this if this is indeed Abaye's opinion?)

Answer: Rather, because this cannot be proven clearly it did not say this. This is why it says it is an argument among the Tanaim. The Gemara cannot ask on Rabah that we cannot say the argument of Rebbi Acha and the Rabbanan is regarding writing carved in wood, and that they must argue regarding whether one will confuse a wall with Shtarei Hedyotos.

Explanation #2 (cont.): However, everyone holds of Rabah because it is logical that if there is writing carved in a wall, the Rabbanan certainly will not say that one will come to confuse reading the writing on this wall with Shtarei Hedyotos. The Beraisa earlier must be referring to a case of carving, according to the opinion that one would normally confuse (regular) writing on a wall with Shtarei Hedyotos.

Question: This explanation has a small difficulty, as it should have said that everyone does not agree with Rabah, and that Abaye and Rav Bibi argue regarding whether one will confuse a wall with Shtarei Hedyotos.

Explanation: It appears that he only said this if the statue was made to be an idol. However, if it was merely made for beauty it is permitted.

Proof: This is as implied by the Gemara in Avodah Zarah (50a) that says that the sons of the holy ones would not look at the image on a coin. This implies that others would look at it.

Explanation #1: Since they are exacting with each other, they transgress what other people would not transgress because of their measurements.

Explanation #1 (cont.): This is as the Gemara states in Beitzah (29a) that a person can say to his friend, "Fill this vessel for me." However, he cannot say an amount (on Yom Tov). This means that he may not use a vessel that has a specific amount, as it is similar to the way business is done. Since these people are exacting, every vessel they own has a specific amount so that they will know that people have to pay them back the amount that this vessel contains.

Explanation #1 (cont.): Similarly, weighing items opposite other items that they are holding in their hands is forbidden, as in Beitzah (ibid.) the Gemara says that (the Rabbanan say) one cannot weigh in any manner (including weighing items opposite vessels and the like, even without a scale).

Explanation #1 (cont.): Counting amounts is also prohibited, as the Gemara says in Beitzah (29b) that a person can go to a merchant who he is familiar with and say, "give me etc." as long as he does not say an amount that he will pay him. If people pay a Dinar for one hundred nuts and he already took ninety, he should not say, "Give me another twenty nuts and I will owe you ten," as it appears he is taking the amount he is taking in order to pay one Dinar. However, he can tell him, "Give me twenty nuts" without saying anything else. If people in a certain group are exacting with each other these behaviors are forbidden, as they will probably end up mentioning in some way (that we have mentioned above) that payment will be required.

Explanation #1 (cont.): According to Beis Hillel there is even a problem of charging interest, as when they return items they borrowed to each other they are exacting regarding what item was worth more.

Question: There is a difficulty according to this explanation. If Hillel is only referring to people who are exacting with each other, why does the Gemara ask earlier that we should say the Mishnah is unlike Hillel? Hillel is only referring to people who are exacting with each other!

Question (cont.): The previous Mishnah can certainly be according to Hillel, as the first part of the Mishnah is referring to people who are not exacting with each other.

Proof: This is apparent from the fact that it says, "One may borrow." People who are exacting with each other cannot borrow according to the explanation above! (The Mishnah therefore must be talking about people who are not exacting!)

Explanation #2: This is why it appears that the Gemara means when it says that they transgress due to measures and weights that they are close to transgressing these prohibitions.

Explanation #2 (cont.): They are close to transgressing measurements since they are exacting with each other, and they will usually borrow from each other an exact amount. Therefore, they will probably still do so even on Yom Tov. While everyone may not borrow in a vessel with an exact amount as stated in Beitzah (29b), Rav Yehudah in our Gemara is giving advice that these types of people should not participate in casting lots for portions, as they will probably come to transgress measuring on Yom Tov.

Explanation #2 (cont.): Similarly, regarding weighing, since they are used to weighing carefully they will not be careful about not weighing on Yom Tov.

Explanation #2 (cont.): Regarding counting units, when one of them borrows sixty nuts, he will tell his friend to give him another forty to total one hundred as he normally would do.

Explanation #2 (cont.): Regarding borrowing and paying back on Yom Tov, we said earlier that saying "loan" instead of "borrow" is prohibited. Since they are exacting with each other, they will say, "loan." The one asking will think that if he says, "borrow" the implication is that I will return it as is. He will therefore say, "loan."

Explanation #2 (cont.): According to Hillel, these people even transgress charging interest. This is because when they borrow from each other they end up charging interest, since the borrower sometimes pays more for the item than the lender. Even though he is exacting about this, he is embarrassed not to pay back exactly what he borrowed because he received benefit. Since the borrower does not forgo the extra amount he must pay, it is considered interest. However, other people do not mind the small extra amount they must pay, and for them it is not considered interest.

Explanation #2 (cont.): The Mishnah therefore is referring to people who are exacting with each other, as most neighbors who are not friends are exacting with each other. Even so, the Mishnah permitted borrowing when it is stated as "borrowing" and not a "loan."

Explanation #2 (cont.): When Rav Yehudah discusses people who are exacting, he is only referring to a group of people who usually borrow from each other and they will therefore end up transgressing. However, neighbors who do not usually borrow from each other may do so, and we do not decree that they will come to transgress.

Explanation #2 (cont.): This is why the Gemara does not answer when it asks that our Mishnah seems unlike Hillel that the Mishnah is referring to people who are not exacting with each other. This is because the Mishnah presumably is discussing people who are exacting with each other as I have explained (that neighbors who are not good friends who borrow from each other often are presumed to be exacting with each other).

Explanation: This is as per the opinion of Rebbi Yehudah in the name of Rebbi Tarfon who says that none of them are a Nazir, as a pledge of Nezirus is only valid when stated clearly. He holds that a person does not enter himself into a doubtful situation.

Opinion: We do not rule like this. Rather, we rule like the other statement of Rebbi Yehudah, as the law is stated in Sanhedrin (25a).

Question #1: This is difficult, as the Gemara in Kidushin (53a) says that one cannot divide sacrifices based on (portions one will receive from) other sacrifices, and flour offerings based on (portions one will receive from) other flour offerings. This is derived from the Pasuk, "And for all sons of Aharon, everyone should get the same as his brother."

Question #2: Additionally, the Gemara asks from the fact that the modest people withdrew their hands from taking, and those who were gluttonous divided. What does this mean that they divided? It means they grabbed etc.

Answer: Rebbi says that dividing and lotteries did not help make these portions of sacrifices into their money to be Mekadesh a woman and to be able to take it away from someone else in Beis Din. However, they would still cast lots to be able to give each person a portion, lest they fight over it. This is as the Pasuk states, "And your nation is like the fights of a Kohen" (Hoshea 4:4).

Implied Question: The Gemara answers that "dividing" really means grabbing, and it does not answer that dividing means a forced division. (If the above answer is correct, why didn't the Gemara itself give this answer?)

Answer: This must be because people indeed grabbed portions that did not belong to them.