DOES ONE FULFILL THE MITZVAH OF TZEDAKAH WITH LESS THAN PERUTAH? [Tzedakah: Shi'ur]
Gemara
59b (R. Yitzchak bar Yosef): If a k'Zayis of Levonah was put on any amount of Minchah, it is Pasul.
(R. Yochanan): "V'Lo Yiten connotes putting a proper Shi'ur. "Aleha" (connotes that putting on a proper Shi'ur of a Minchah. It says "Aleha" regarding the Isur to put oil, and regarding the Isur to put Levonah.) Whenever two sources include the same thing, they actually come to exclude. (I.e., one who puts on any amount of Minchah transgresses.)
Question (R. Yitzchak bar Yosef): If any amount of oil was put on a k'Zayis of Minchah, what is the law? Must 'Simah' (of oil) resemble 'Nesinah' (of Levonah, which connotes a k'Zayis?)
This question is not resolved.
Bava Metzi'a 31b - Question: Perhaps "Nason Titen" applies only to a big gift. What is the source that it applies even to a small gift?
Answer: "Nason Titen" teaches any case.
55a (Mishnah): A Perutah is the Shi'ur for five things: the admission (for the oath of partial admission); money to be Mekadesh a woman; benefit from Hekdesh to transgress Me'ilah...
Pesachim 32b (Beraisa): If a Zar ate a k'Zayis of Terumah (b'Shogeg), he pays Keren v'Chomesh;
Aba Sha'ul says, he pays only if he ate the value of a Perutah.
The first Tana learns from "v'Ish Ki Yochal Kodesh bi'Shgagah." The Shi'ur of 'Achilah' (eating) is a k'Zayis. Aba Sha'ul's learns from "v'Nosan (la'Kohen Es ha'Kodesh)." The Shi'ur of 'Nesinah' (giving) is a Perutah.
Bava Basra 9a (Rav Asi): One should give at least a third of a Shekel to Tzedakah every year - "we established Mitzvos upon ourselves... Shelishis ha'Shekel b'Shanah."
9b (R. Yitzchak): One who gives a Perutah to a poor person gets six Berachos.
Rishonim
Sefer ha'Yir'ah: One should regularly give Tzedakah according to his ability. He should obligate himself to redeem his soul every week, a Perutah or half. Even an Oni financed from Tzedakah must do Tzedakah.
Tosfos (Pesachim 32b DH v'Ein): Aba Sha'ul holds that 'Nesinah' is at least a Perutah. Chachamim disagree only because it says 'Achilah'. We hold that one piece of wheat exempts the entire stack (for Terumah), even though it says 'Nesinah'! We acquire with a Kli even though it is worth less than a Perutah, even though it says "he gave to his fellowman." A Get on Isurei Hana'ah is Kosher, even though it says "v'Nasan b'Yadah." We can answer that Nesinah of payment must be a Perutah, like returning theft, which must be at least a Perutah. Other places (that are not payment), even though it says Nesinah, do not require a Perutah. In Kerisus (6b), regarding putting Shemen ha'Mishchah on a Zar, R. Yehudah learns from Terumah to require a k'Zayis. He should be stringent to say that it is any amount, like we find regarding Zerikah, and putting blood and oil on the thumbs and toes of a Metzora, which is like anointing. This is not difficult for the opinion that argues with R. Yehudah and obligates for any amount.
YAd Eliyahu: The Torah wanrs not to refrain from lending shortly before Shemitah, even though this is like a gift, for Shemitah will cancel the loan. If so, why do we need a verse to obligate a small gift? All the more so one must give a small amount! It is difficult to say that surely the Oni would voluntarily return a large loan (even though Shemitah cancelled it), lest he deter people from lending. He would not return a small loan, for it is clearly like a gift, just he requested a loan because he was ashamed to request a gift.
Note: It is not clear to me why this is like a gift. We hold that if a loan was not due until after Shemitah, Shemitah does not cancel it. If one requests a loan just before Shemitah, and almost surely he will not pay before Shemitah, the lender could stipulate that it is not due until after Shemitah! (The Rosh holds that the entire year is Meshamet. If so, a lender would need to stipulate that it is not due for over a year. Even so, if he wants to be repaid, this is better than giving a (nearly) certain gift.) The Torah warns not to refrain from lending, for most people want prompt payment, and then they risk cancellation of the loan.
Tosfos (Menachos 60a): Chachamim learn from payment of Terumah that Nesinah is a k'Zayis. Aba Sha'ul says that it is a Perutah, i.e. even if there is not a k'Zayis. perhaps Aba Sha'ul agrees that normally, Nesinah is a k'Zayis. Payment for Terumah is different; we learn it from Me'ilah.
Poskim
Shulchan Aruch (YD 249:2): One should not give less than a third of a Shekel each year to Tzedakah. If he gave less, he did not fulfill the Mitzvah.
Shach (4): The custom is that the Gabai collects on Monday and Thursday from everyone. Even if one gives the smallest coin, over the course of a year he gives a third of a Shekel.
Mishneh Halachos (7:157, citing Beis Yitzchak OC 21): In Bava Metzi'a, we suggested that "Nason Titen" refers only to a big gift. The Gemara expounded the repetition to teach even about a small gift. Beis Yitzchak explained this like it says in Menachos. Two exclusions come to include. Here also, first we discuss a (big) Nesinah of a k'Zayis or Perutah, and later include less than a Perutah. One who gives a Perutah to an Oni gets six Berachos. It is not precise; the same applies to less than a Shavah Perutah. Alternatively, the Berachos are only for one who gives an important amount, but the Mitzvah is even for less than a Shavah Perutah. The Shach connotes that there is a Mitzvah to give even less than a Shavah Perutah.
Note: A Shekel is 384 Perutos. The Shach said that if one gives every Monday and Thursday, in one year (about 100 times) he will give at least a third of a Shekel (128 Perutos). His calculation is based on the premise that the smallest coin is more than a Perutah!
Rebuttal (Mishneh Halachos): In many places, the Gemara, Rambam and Shulchan Aruch mention giving a Perutah to Tzedakah, and that every Perutah joins (to a big amount). It did not mention giving any amount, or 'every half-Perutah joins'! The Torah said "do not begrudge" when you give Tzedakah. A Yisrael pardons less than a Shavah Perutah. If one fulfills Tzedakah with less than a Shavah Perutah, there is no need to say "do not begrudge"!
Note: Perhaps the Gemara discusses Perutah to teach even the smallest amount of money that one could give, i.e. the smallest coin there is! Rav Yosef (Kidushin 12a) holds that this is a Perutah even for Kidushin! Perhaps all agree that normally, there was no coin less than a Perutah! Likewise, one who guards an Aveidah saves 'Perutah d'Rav Yosef' (Nedarim 33b), i.e. he is exempt from giving Tzedakah. I.e. normally this is the smallest amount that one would give.
Mishneh Halachos: Perhaps the Shach praised the custom to collect every Monday and Thursday, for the half-Perutos join, but one does not fulfill a Mitzvah through a half-Perutah alone! Many Acharonim say that less than a Perutah is money, just Yisre'elim pardon it. When pardon does not apply, there is no reason why it should not join! The Magid Mishneh says that one may not steal less than a Shavah Perutah, for it can join (if the victim does not find out in between). Surely, according to the opinion that Tzedakah is like Hekdesh, it is improper to give less than a Shavah Perutah. Sefer ha'Yir'ah says that less than a Shavah Perutah is a Mitzvah. this is difficult. Bava Metzi'a discussed first a large gift, and afterwards giving even a Perutah.
Torah Lishmah (ibid.): If one separated half a Perutah, gave it to an Oni, and later separated another half Perutah and gave it to another Oni, he was not Yotzei. Perhaps it depends on the recipient, and neither Oni received a Perutah. If he gave both to the same Oni, it seems that he was Yotzei even though he did not give them together. A Shi'ur of time applies only for eating, i.e. in the time to eat half a loaf. There is no Shi'ur for giving Tzedakah. If he gave half a Perutah in the morning and another half Perutah in the evening, why shouldn't they join?! Shevu'os 38b proves this. If one claimed a deposit, wages, theft and Aveidah from Ploni, worth a Perutah in all, they join. Likewise, wheat and barley join to a Perutah. One who swore falsely about this is liable. Even though he did not get the Perutah at once or for one reason, they join, since now the parts are together. Similarly, now the Oni benefits a Perutah. However, perhaps this is only if he still has the first half-Perutah when he receives the second. If he already ate the first, its Hana'ah passed and it is Batel, as if it never was. If one waited more than Kdei Achilas Pras between eating one half k'Zayis and another, they do not join. The same applies here. Do not learn from Pidyon ha'Ben. If one gave five Sela'im in all to 10 Kohanim, even one after the other, his son is redeemed (YD 305:7). There, everything he gave is considered money, just it is a Chetzi Shi'ur of the Mitzvah. Here, each part is not considered money, and has no significance. Likewise, one cannot learn from Shofar. If one heard the nine blasts over the course of the day, he was Yotzei, even from nine people. They jopin, even though they are Me'akev each other, because each is important by itself.
Torah Lishmah (ibid.): We can learn from Kidushin. If one was Mekadesh a woman with dates, and said 'with this and this and this', and she ate them and never had the value of a Perutah at once, she is only Safek Mekudeshes (lest even one was worth a Perutah somewhere else). If he said 'with these', she is Mekudeshes if in all they are Shavah Perutah, even if she ate them and never had a Perutah at once (Kidushin 47a, EH 31:6). This shows that also regarding Tzedakah, they join. Even when he said 'with this and this and this', they join; she is not Mekudeshes only because a loan is not Mekadesh.
Shnos Eliyahu (Pe'ah 1:1): The Yerushalmi says that there is no Shi'ur to Chesed with one's body, but there is a Shi'ur of monetary Chesed. A Mishnah says that one should not give more than a fifth; this is mid'Oraisa. The Gemara says that they enacted this in Usha, i.e. it was a tradition from Moshe from Sinai, then it was forgotten, and they re-established it like the initial Halachah.
Ateres Paz (YD 10, Ha'arah 4): According to those who say that this is a tradition from Sinai, Tzedakah has a limit from the Torah. One opinion in the Yerushalmi says that the Shi'ur is like Terumah. Tzaafnas Pane'ach (Hilchos Matanos Aniyim 9:1) says that less than a Shavah Perutah is not Tzedakah. Maharil Diskin (Pesakim 24, Ha'arah DH Teda) says that it is a Mitzvah. The Shulchan Aruch said that giving a Perutah fulfills the Mitzvah of Tzedakah. it does not exclude less than a Shavah Perutah. If not, it should have been included with the five matters for which the Shi'ur is a Perutah! Beis Yitzchak learns from Tosfos in Menachos that giving is always at least a Perutah. Only Get need not be Shavah Perutah, for "Sefer" connotes of any valuie. Since it says Nesinah regarding Tzedakah, less than a Shavah Perutah is not a Mitzvah. However, Tosfos (Pesachim 32b DH v'Ein) connotes that it is a Mitzvah.