We know that all 12 tribes of Israel (The tribe of Benjamin and Judah plus the 10 lost tribes) were given the Torah at Mount Sinai. And we know that since the destruction of the first temple all tribes were scattered throughout the world. So It would be safe to assume that today there are hundreds of millions of modern day Israelites (not part of Judah but part of the other lost tribes of Israel) that are descended from at least one of these tribes and don't even know it. Therefore, would anyone descended from one of the 10 lost tribes of Israel still be obligated to keep the 613 mitzvot to this day? (barring the fact that its not possible for all commandments to be kept at this time)
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P(extinction by gen. n) = G(P(extinction by gen n-1)), so asn->∞,P(Ultimate Extinction) = G(P(Ultimate Extinction)).x = G(x). Therefore if we weigh the probabilities of how many girls each generation has, and solve, we note that the answer has to be larger than 1. I.e. if each family had an average of one Jewish girl, or less, then they would definitely go extinct. If more than 1, they still might go extinct, but not guaranteed. The math of extinction is very conterintuitive, but it seems impossible that any made it this many generations. – Rabbi Kaii Feb 11 '24 at 13:30