Any descendent1 of Noah (Noahide) who takes upon himself to keep those seven commandments and is careful to do them is [considered as] one of the righteous among the nations of the world, and has a share in the world to come. It is added there to say, that only does he merit entry into the world to come through them, when he accepts to do them because God, the Blessed, commanded them in the Torah, and we were informed by Moses our teacher that they were commanded [to uphold] them. However, if he does them out of a sense of judgment, he is not one of the righteous among the nations of the world, nor is he one of their sages.
שבן נח המקבל על עצמו לקיים אותן שבע מצות ונזהר לעשותן, הרי זה מחסידי אומות העולם, ויש לו חלק לעולם הבא, אמנם הוסיף שם לומר, שרק אז זוכה על ידן לעולם הבא, כשמקבל לעשותן מפני שצוה בהן הקב"ה בתורה, והודיענו על ידי משה רבינו שב"ן נצטוו בהן, אבל אם עשאן מפני הכרע הדעת אינו מחסידי אומות העולם ולא מחכמיהם
We have already shared a number of things related to Rabbi Yonasan Steif’s sefer Miztvot Hashem; we have decided to share here yet another important teaching. In the introduction2 to part 2 dealing with laws between man and his fellow man, Rabbi Steif teaches us an important message about the nations of the world and their acceptance of the 7 mitzvot3, it has to be accepted as something instructed from Hashem himself; if they choose to follow the mitzvot because they make logical or rational sense, then those individuals are not considered from the righteous of the nations.
What is Rabbi Yitzchok Dovid Smith’s Vision
80 Billion men and women serving G-d Al-mighty with the spiritual leadership of the Jewish People and a fully built and functioning Beis HaMikdash in Yerushalayim.
end of section 28.
End of Sanhedrin 56a. Though not taught explicitly in the Torah as one cohesive unit, the are several different references and allusions to the 7 mitzvot. To briefly review they are
Prohibition on Idol Worship
Prohibition on Murder
Prohibition on Sexual Immorality
Prohibition on Tear a Limb from a Living Animal
Prohibition on Cursing the Name of G-d Al-mighty
Prohibition on Stealing
Requirement to setup and enforce Courts and Educational Systems
Literally ‘son.’ Since all of humanity descends from Noah this then technically refers to all of humanity, since the Children of Israel, or Jews, are a subset of this they are included in all the laws that apply, however, because of their obligation to keep ALL of the Torah, they are considered separately, and then the term descendent of Noah, or Noahide is used to refer to all humanity except the children of Israel.