(Rav Nachman): An egg does not forbid a mixture 60 times its own size. It itself is not counted towards 60.

Question (Rav Idi bar Avin): This implies that eggs give Ta'am. However, people say that egg water (i.e. in which eggs were cooked) is like plain water!

Answer (Abaye): The case is, there was a chick inside the egg.

Inference: Tamei eggs (i.e. of a Tamei bird) would not forbid a mixture.

Question (Beraisa): If Tamei eggs were cooked with and gave Ta'am to Tahor eggs, all are forbidden.

Answer: 'Tamei' eggs means eggs with a chick inside.

Question (Seifa): If eggs were cooked and a chick was found inside one of them, if it gave Ta'am to them, they are all forbidden.

This implies that the Reisha does not discuss chicks in eggs!

Answer: The Seifa explains the Reisha;

(Beraisa): If Tamei eggs were cooked with and gave taste to Tahor eggs, all are forbidden;

The case is, a chick was found inside one of them.

Support: The Reisha cannot discuss when no chick is inside, for then the Seifa would not need to forbid them when a chick is found in one!

Rejection: No, the Seifa must say so, lest we think that in the Reisha, a chick is inside.

Since in the Seifa a chick is inside, the Reisha must discuss when no chick in inside, and even so they are forbidden.

A k'Zayis of Chelev fell into a pan of meat. Rav Ashi thought to include what had been absorbed by the pot in the calculation of whether or not there was enough Heter to be Mevatel the Chelev.

Rabanan: The pot absorbed also Chelev! (If you will reckon with absorbed Heter, you should also assume that there was more than the k'Zayis of Chelev we see now.)

A half-k'Zayis of Chelev fell into a pan of meat. Mar bar Rav Ashi thought that if there was 30 times as much Heter, it would be Mevatel the Chelev.

Rav Ashi: Do not be lenient about the quantities that Chachamim fixed (i.e. 60 times);

Also, you must be stringent because R. Yochanan forbids mid'Oraisa even less than a Shi'ur (the quantity for which one gets lashes or Kares, i.e. k'Zayis).

(Rav Shemen bar Aba): A (forbidden) egg among 60 forbids all of them;

If it is among 61, they are permitted.

R. Zeira: People will understand that you permit if there are 61 eggs including the forbidden egg. Two giants of the generation were unsure about this!

(R. Yakov bar Idi and R. Shmuel bar Nachmani, citing R. Yehoshua ben Levi): A (forbidden) egg among 60 forbids all of them;

If it is among 61, they are permitted.

Question: Is the forbidden egg among the 61, or not?

They were unable to answer.

(R. Chelbo): If 60 permitted eggs and one forbidden egg became mixed, they are forbidden;

If 61 permitted eggs and one forbidden egg became mixed, they are permitted.

Version #1 (Rashi's Rebbi): A man came in front of R. Gamliel ben Rebbi. Half a k'Zayis of Isur had become mixed with 45 times as much Heter.

R. Gamliel: My father permitted one part in 47 (of Isur. This shows that we do not need 60.) I can permit 45. (Yerushalayimi (cited by Tosfos 64b Gi'ulei) - the shells help to comprise 60 times the volume of Isur.)

A similar case occurred with R. Shimon ben Rebbi.

R. Shimon: My father permitted one part in 45. I can permit 43.

Version #2 (Rashi): A man came in front of R. Gamliel ben Rebbi. Isur was mixed with 45 times as much Heter.

R. Gamliel: My father forbade one part in 47. Should I permit 45?!

A similar case occurred with R. Shimon, the son of Rebbi.

R. Shimon: My father did not permit one part in 45. Should I permit 43?! (end of Version #2)

A man came in front of R. Chiya;

R. Chiya: There isn't 30 times as much Heter as Isur!

Question: If there would have been, would he have permitted it?

Answer (R. Chanina): No. He said that there isn't even 30 times as much Heter. (Even then, it would be forbidden!)

(R. Chiya bar Aba, citing Bar Kapara): Any Isur in the Torah is Batel among 60 parts of Heter (if the Isur cannot be tasted).

(R. Shmuel bar Rav Yitzchak): Rav Asi cited Bar Kapara to say that it is Batel among 100 parts of Heter.

Both opinions learn from (Bitul of) the foreleg of Eil Nazir - "v'Lakach ha'Kohen Es ha'Zero'a Beshelah" (the Kohen gets the cooked foreleg);

(Beraisa): "Beshelah" teaches that it (the foreleg) is cooked whole;

R. Shimon says, this teaches that it is cooked with the ram.

Version #1: All agree that it is cooked with the ram. They argue only about whether it is cut off before or after cooking. (Rashi - Chachamim say that it is first cut off. Tosfos - R. Shimon says so.)

Version #2: All agree that it is cut off before cooking. They argue about whether or not it is cooked with the ram. (Chachamim say that it is not, and R. Shimon says that it is.)

According to Version #1, all agree that it is cooked with the ram. Even though the Zero'a is forbidden to Zarim, the rest of the ram is permitted to anyone. I.e., the Ta'am of the Zero'a is Batel in the ram.

According to Version #2, we learn this from R. Shimon.

The opinion that says 60 times learns from Bitul of the taste of the meat and bones of the foreleg amidst the meat and bones of the ram (which are 60 times as much);

The opinion that says 100 times learns from Bitul of the meat of the foreleg among the meat of the ram (which is 100 times as much. We ignore the bones, for they do not give or absorb Ta'am.)

Question: Do we really learn from the Zero'a to other Isurim?

(Beraisa): This is the case of something forbidden becoming permitted.

Suggestion: 'This' excludes other Isurim!

Answer #1 (Abaye): The Beraisa is like R. Yehudah, who says that Min b'Mino (an Isur mixed with Heter that looks and tastes the same) is never Batel. The Zero'a is the only exception.

Question: We should learn from the Zero'a to other cases!

Answer: (On Yom Kipur, we mix the bloods of the goat and bull that are offered in the Kodesh ha'Kodoshim.) Dam ha'Sa'ir is not Batel in Dam ha'Par, even though the bull has more blood. This teaches that Min b'Mino is never Batel.

Question: Why do we learn from the bloods, and not from the Zero'a (which is Batel)?

Answer: Zero'a is a Chidush (we Mevatel an Isur l'Chatchilah), so we may not learn from it.

Question: If so, we should not learn from it that an Isur (that cannot be tasted) is Batel in 60 or 100 parts of Heter!

Answer: We may not learn leniencies from a Chidush. Requiring 60 or 100 parts is a stringency;

Mid'Oraisa, an Isur is Batel in any majority!

Answer #2 (Rava): Regarding other Kodshim, Ta'am k'Ikar (if Isur mixed with Heter can be tasted, the Heter is forbidden.) Here, Ta'am k'Ikar of the Zero'a (absorbed in the ram) is Batel.