The process of transmission is one of education in the broadest sense, so that what is transmitted is not merely knowledge but beliefs and values, attitudes and ideals, and above all, a sense of identification and commitment. God established a testimony in Jacob and appointed a law in Israel, and commanded our ancestors to teach their children, that the next generation might know them, even the children yet unborn, and arise and tell them to their children, so that they should set their hope in God and not forget the works of God, but keep the commandments.
Reality is one thing, law another.
The extent to which Judaism is actually transmitted varies infinitely. Therefore in reality, Judaism is a matter of degree. Law, however, cannot take account of all the variations and degrees. However, it is desirable that the legal definition should correspond as closely as possible to the real situation. In at least one respect the earlier biblical understanding of Jewish identity differed from the later Rabbinic one.