Gemara

58b (Beraisa) Suggestion: Perhaps if one took 10 animals to be Ma'aser on 100, or one to be Ma'aser on 10, they are Ma'aser!

Rejection: It says "Asiri". These are not tenths.

R. Yosi b'Rebbi Yehudah says, it is Ma'aser.

He holds like Aba Elazar ben Gomel;

(Beraisa - Aba Elazar ben Gomel): It says "v'Nechshav Lachem Terumaschem (ka'Dagan Min ha'Goren)." This refers to (and equates) two Terumos, i.e. Terumah Gedolah and Terumas Ma'aser;

Just like Terumah Gedolah is taken by estimation and Machshavah (mere intent), also Terumas Ma'aser.

27a (Shmuel): One may eat Tevel of Chutz la'Aretz, leave over the amount needed for Terumah, and later designate the remainder to be Terumah.

Shabbos 34a (Mishnah): Bein ha'Shemashos (Safek day, Safek night (Shabbos)), one may not tithe Vadai (definite) Tevel, but one may tithe Demai (Safek Tevel).

141b (Mishnah): One may move Tamei Terumah with Tahor Terumah or with Chulin;

R. Yehudah says, if there are (in Meduma, i.e. a mixture of Terumah and Chulin has) at least 101 (volumes of mixture per volume of Terumah), one may even be Ma'aleh the Meduma on Shabbos. (He removes an amount equal to the Terumah, treats it like Terumah, and the rest is permitted like Chulin.)

142a - Question: Why does R. Yehudah permit this? He fixes (permits) the Meduma!

Answer: He holds like R. Shimon ben Elazar:

(Beraisa - R. Shimon ben Elazar): One may put his eyes on one side of Meduma (intend that it is the Terumah) and eat from the other side. (Since one may eat it without separating, separating is not considered Tikun.)

Question: R. Yehudah does not hold like R. Shimon ben Elazar!

(Beraisa - R. Yehudah): We may be Ma'aleh Meduma if there is 101 (in the mixture);

R. Shimon ben Elazar says, he puts his eyes on one side and eats from the other side. (He may not separate it.)

Answer: Indeed, R. Yehudah is more lenient than R. Shimon ben Elazar.

Chulin 6b: R. Yehoshua ben Zeruz testified that R. Meir ate a leaf of a vegetable from Beis She'an without separating Ma'aseros. Based on this, Rebbi exempted Beis She'an from Ma'aseros.

7a - Question (R. Yirmeyah): Perhaps R. Meir designated that the tithes take effect on produce that he had elsewhere!

Answer (R. Zeira): A Chaver always tithes Min ha'Mukaf (near the food being exempted).

Question (R. Yirmeyah): Perhaps he put his eyes on one side and ate from the other side!

Answer (R. Zeira): A great man testified about this. Surely he gave all the pertinent details, lest we learn the wrong law from it!

Rishonim

Rambam (Hilchos Shabbos 24:10): Bein ha'Shemashos one may do Shevus (an Isur mid'Rabanan of Shabbos) only if needed for a Mitzvah, or in pressed circumstances. Therefore one may not tithe Vadai Tevel, even though this is only Shevus, but one may tithe Demai.

Rashi (59a DH b'Machshavah): This (separating one on 10, or 10 on 100) is called intent, because he does not count them.

Tosfos (Gitin 31a DH Kach): Rashi explains that regarding estimation we learn Terumas Ma'aser from Terumah Gedolah, but for separating through intent, both are learned from v'Nechshav. Alternatively, also for intent we learn Terumas Ma'aser from Terumah Gedolah. Even though it says v'Nechshav, since it says "k'Degen Min ha'Goren", which is Terumah Gedolah, i.e. the first Degen (grain) that one separates from the granary, the verse equates Terumas Ma'aser to it also regarding intent. It seems that Rabanan argue with Aba Elazar only about estimation, but not about intent, for the verse teaches this. In Kidushin (41b) we ask 'just like Terumah is taken through mere intent...' This implies that all agree to this. This refers to Terumas Ma'aser, about which it says "Gam Atem" (from which the Gemara there learned Shelichus). This is unlike Rashi, who says that we establish R. Yosi b'Rebbi Yehudah like Aba Elazar because he holds that intent suffices. The Sugya is unlike this. R. Yosi b'Rebbi Yehudah's law is not related to intent!

Tosfos (31a DH b'Machshavah): Rashi explains that he puts his eyes on one side (intends that it be Terumah) and eats from the other side, even without (physically) separating. I.e. one may eat without separating, even if he was silent. We learn all this from v'Nechshav. Indeed, it is Terumah without speech. The Mishnah (Terumos 1:6) says that b'Di'eved, Terumah of a mute person takes effect. The Yerushalmi explains that it is b'Di'eved because he cannot bless. In Shevu'os (26b) we say that Terumah and Kodshim are Shenei Kesuvim (two verses), both of which teach that it suffices to resolve in one's heart, even without speaking, therefore we do not learn oaths from them. All agree about all Ma'aseros that one may eat without a physical separation, even Ma'aseros for which it does not say v'Nechshav. This is clear from the case of one who buys wine from Kusim (Gitin 25a). (R. Meir permits drinking before separating.) Those who disagree forbid only because they do not rely on Breirah, or due to concern lest the barrel break and he will never separate (so retroactively, he drank Tevel). For Ma'aser Sheni, it suffices to say that it is in the north or south.

Question: Since we permit (Tevel to) Terumah through intent, why is it forbidden to tithe on Shabbos? R. Yehudah permits to be Ma'aleh Meduma because one may put his eyes on one side eat from the other side. Since one may eat through mere intent, separating is not considered Tikun. Here also, it is possible through mere intent!

Answer (Tosfos): Meduma is different, for it was already fixed. We do not permit the initial fixing of Tevel just because it is possible through intent. One may not fix even Demai on Shabbos (Shabbos 34a), even though one may put his eyes on one side and eat from the other side (Chulin 7a).

Rebuttal (R. Akiva Eiger 59a DH b'Machshavah): In Shabbos, we say that R. Yehudah is more lenient than R. Shimon (ben Elazar). R. Shimon permits only to put his eyes on one side and eat from the other side. R. Yehudah holds that since one may do so, separating is not Tikun. We can say that Shabbos 34a is like R. Shimon ben Elazar. Perhaps Rabanan who argue with R. Yehudah in the Mishnah, permit to put his eyes on one side and eat from the other side for Meduma, but even so they call this Tikun. R. Yehudah holds that this is not called Tikun. The Ramban in Beitzah says that R. Yehudah's colleagues hold that even so (that one may put his eyes on one side and eat from the other side), one may not be Korei Shem. If so, Tosfos' question is not difficult.

Poskim

Shulchan Aruch (YD 331:46): If one separated Terumah mentally without saying a word, it is Terumah, for it says "v'Nechshav Lachem Terumaschem."

Shach (76): In Sa'if 45, he intended to say Terumah and (mistakenly) said Ma'aser. It does not take effect because his words negated his intent. Here, there is no contradiction.

Gra (92 Likut): Even though we could say that Demai is different (but normally, one may not put his eyes on one side and eat from the other side), we do not distinguish like this. A proof that Chulin 7a discusses Vadai Tevel is that we said that a Chaver would never tithe Lo Min ha'Mukaf. This is only for Vadai Tevel, but it is permitted for Demai, like it says in Chalah 4:6. (R. Shimshon there says that this is only for Demai of Chalah, but not for regular Demai, like we find in Chulin. Even though R. Meir ate Demai, like R. Tam says, he would not tithe Lo Min ha'Mukaf.) R. Yehudah permits fixing only Meduma on Shabbos. R. Shimon (ben Elazar) forbids. The first Tana forbids even to put his eyes on one side eat from the other side., since we say that R. Yehudah holds like R. Shimon (i.e. but not like Chachamim). If one was Korei Shem (verbally designated) before Shabbos, all permit separating it on Shabbos. All of this applies also to Chalah.

Shulchan Aruch (OC 261:1): Bein ha'Shemashos one may not tithe Vadai Tevel, but one may tithe Demai.

Beis Yosef (DH Safek): Rashi explains that one may not tithe Vadai, for this is a great Tikun. The Tana of the Mishnah forbids Shevus Bein ha'Shemashos. Since we hold like the opinion that permits Shevus Bein ha'Shemashos, one may tithe Vadai. However, the Tur permits only for needs of a Mitzvah or if he was very busy, like the Rambam. It seems that Rashi disagrees. If not, our Tana could permit Shevus Bein ha'Shemashos, and he forbids tithing Vadai when it is not a Mitzvah and he is not busy! Perhaps because our Mishnah forbids Stam, i.e. in every case, Rashi says that the Tana forbids Shevus Bein ha'Shemashos. We hold like the Rambam.

Beis Yosef (Sof ha'Siman DH u'Mah): Rashi explains that one may tithe Demai for it does not resemble Tikun, since most Amei ha'Aretz tithe. (It is probably tithed already.)

Mishnah Berurah (3): One may not even tithe fruits, for which Ma'aser is mid'Rabanan.

Mishnah Berurah (4): Similarly, one may not separate Chalah even in Chutz la'Aretz. Chalah of Chutz la'Aretz is more stringent than Ma'aser. If one has no food to eat on Shabbos, this is needs of a Mitzvah, so Chachamim permit Shevus (tithing) Bein ha'Shemashos. We are always stringent about Chalah, since one may eat Chalah of Chutz la'Aretz without separating. He leaves some until after Shabbos, and separates from what remains.

Kaf ha'Chayim (4): Some permit separating Chalah of Chutz la'Aretz Bein ha'Shemashos, but others forbid, since one may eat and separate afterwards. One may separate Chalah of Eretz Yisrael Bein ha'Shemashos if he has no other bread, for it is a Mitzvah, and Chachamim did not decree Bein ha'Shemashos.

Avi ha'Ezri (Teshuvos u'Bi'urei Sugyos 937 DH v'Hach): The 'Machshavah' we discuss here is speech. (It is not clear whether the Machshavah of Kodshim is verbal.) One may not separate tithes even on Yom Tov. We must say that one may not put his eyes on one side and eat from the other side. Rather, the Machshavah is a physical separation, but he is Korei Shem in his heart, but not verbally. One may put his eyes on one side and eat from the other side only for Meduma, which is mid'Rabanan, so Chachamim were lenient. One may eat Tevel of Chutz la'Aretz, and leave over and tithe from the remainder. We rely on the Heter to put his eyes on one side and eat from the other side, for the entire source of Terumah of Chutz la'Aretz is mid'Rabanan. The source of Demai is mid'Oraisa, so we are stringent, even though most Amei ha'Aretz tithe. One may not tithe it on Shabbos, nor put his eyes on one side and eat from the other side.