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(י) משֶׁה רַבֵּנוּ לֹא הִנְחִיל הַתּוֹרָה וְהַמִּצְוֹת אֶלָּא לְיִשְׂרָאֵל. שֶׁנֶּאֱמַר (דברים לג, ד) "מוֹרָשָׁה קְהִלַּת יַעֲקֹב". וּלְכָל הָרוֹצֶה לְהִתְגַּיֵּר מִשְּׁאָר הָאֻמּוֹת. שֶׁנֶּאֱמַר (במדבר טו, טו) "כָּכֶם כַּגֵּר". אֲבָל מִי שֶׁלֹּא רָצָה אֵין כּוֹפִין אוֹתוֹ לְקַבֵּל תּוֹרָה וּמִצְוֹת. וְכֵן צִוָּה משֶׁה רַבֵּנוּ מִפִּי הַגְּבוּרָה לָכֹף אֶת כָּל בָּאֵי הָעוֹלָם לְקַבֵּל מִצְוֹת שֶׁנִּצְטַוּוּ בְּנֵי נֹחַ. וְכָל מִי שֶׁלֹּא יְקַבֵּל יֵהָרֵג. וְהַמְקַבֵּל אוֹתָם הוּא הַנִּקְרָא גֵּר תּוֹשָׁב בְּכָל מָקוֹם. וְצָרִיךְ לְקַבֵּל עָלָיו בִּפְנֵי שְׁלֹשָׁה חֲבֵרִים. וְכָל הַמְקַבֵּל עָלָיו לָמוּל וְעָבְרוּ עָלָיו שְׁנֵים עָשָׂר חֹדֶשׁ וְלֹא מָל הֲרֵי זֶה כְּמִן הָאֻמּוֹת:

(10) Moses our Teacher did not bequeath the Torah and the Commandments to anyone but to Israel, as it says, “the Heritage of the Congregation of Jacob” (Deut. 33:4), and to anyone from the other nations who wishes to convert, as it says, “as you, as a convert” (Numbers 15:15). However, no one who does not want to convert is forced to accept the Torah and the Commandments. Moses our Teacher was commanded by the Almighty to compel the world to accept the Commandments of the Sons of Noah. Anyone who fails to accept them is executed. Anyone who does accept them upon himself is called a Convert Who May Reside Anywhere79A “Resident Convert” for short. He may live anywhere in the Land of Israel.. He must accept them in front of three wise and learned Jews. However, anyone who agrees to be circumcised and twelve months have elapsed and he was not as yet circumcised is no different than any other member of the nations of the world80He remains a non-Jew in every respect..

(יא) כָּל הַמְקַבֵּל שֶׁבַע מִצְוֹת וְנִזְהָר לַעֲשׂוֹתָן הֲרֵי זֶה מֵחֲסִידֵי אֻמּוֹת הָעוֹלָם. וְיֵשׁ לוֹ חֵלֶק לָעוֹלָם הַבָּא. וְהוּא שֶׁיְּקַבֵּל אוֹתָן וְיַעֲשֶׂה אוֹתָן מִפְּנֵי שֶׁצִּוָּה בָּהֶן הַקָּדוֹשׁ בָּרוּךְ הוּא בַּתּוֹרָה וְהוֹדִיעָנוּ עַל יְדֵי משֶׁה רַבֵּנוּ שֶׁבְּנֵי נֹחַ מִקֹּדֶם נִצְטַוּוּ בָּהֶן. אֲבָל אִם עֲשָׂאָן מִפְּנֵי הֶכְרֵעַ הַדַּעַת אֵין זֶה גֵּר תּוֹשָׁב וְאֵינוֹ מֵחֲסִידֵי אֻמּוֹת הָעוֹלָם וְלֹא מֵחַכְמֵיהֶם:

(11) Anyone who accepts upon himself and carefully observes the Seven Commandments is of the Righteous of the Nations of the World and has a portion in the World to Come. This is as long as he accepts and performs them because (he truly believes that) it was the Holy One, Blessed Be He, Who commanded them in the Torah, and that is was through Moses our Teacher we were informed that the Sons of Noah had already been commanded to observe them. But if he observes them because he convinced himself logically81By his own intellect and conscience, but he does not agree that they were commanded by G-d., then he is not considered a Resident Convert and is not of the Righteous of the Nations of the World, but merely one of their wise.

(ה) ועוד אמרו זכרונם לברכה (שם מ''ד) בענין זה שהגרים אף על פי שלא נתחלקה להם הארץ מביאין וקורין, כי לאברהם נתנה תחלה והוא נקרא אב המון גוים (בראשית יז ד), כלומר שכל המתגיר נחשב לו כבן.

(5) And they, may their memory be blessed, also said (Mishnah Bikkurim 1:4) about this matter that converts bring them and recite, even though the land was not distributed to them. As it was given to Avraham first, and he was called "the father of many nations" (Genesis 17:4) - meaning to say that anyone who converts is considered like his son.

א"ר יוחנן משום ר"ש בן יוחי דאמר קרא (דברים ז, ד) כי יסיר את בנך מאחרי בנך הבא מישראלית קרוי בנך ואין בנך הבא מן העובדת כוכבים קרוי בנך אלא בנה
Rabbi Yoḥanan says in the name of Rabbi Shimon ben Yoḥai: As the verse states with regard to the same issue: “Your daughter you shall not give to his son…for he will turn away your son from following Me” (Deuteronomy 7:3–4). Since the verse is concerned that after one’s daughter marries a gentile, the father will lead his children away from the service of God, this indicates that your son, i.e., your grandson, from a Jewish woman is called “your son” by the Torah, but your son from a gentile woman is not called your son, but her son.
אמר רבינא ש"מ בן בתך הבא מן העובד כוכבים קרוי בנך נימא קסבר רבינא עובד כוכבים ועבד הבא על בת ישראל הולד ממזר
Ravina said: Learn from it that the son of your daughter, born to a gentile, is called your son in all regards. The Gemara asks: Shall we say that Ravina holds that with regard to a gentile or a Canaanite slave who engaged in sexual intercourse with a Jewish woman, the offspring is a mamzer? One can infer from the fact that the offspring of this union is called “your son” that he is a Jew, and therefore the principle stated in the mishna should apply: If a woman cannot join in betrothal with someone, their child is a mamzer.