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No Ammonite or Moabite shall be admitted into the congregation of the Lord; none of their descendants, even in the tenth generation-Deuteronomy 23:4

What is the significance of the ten-generation number that the torah uses in this verse? What is it about ten in this context that makes it significant?

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With regards to a mamzer (Devarim 23:3), see this blog post on Yevamos 78 :

Reb Yonasan Eibshitz explains: Up until ten generations, the strength of the father still exists in his descendants.

The Vilna Gaon states: A father and mother are equal partners in a child. A grandson would have twenty-five percent from the father. The third generation will have an eighth. The fourth will have a sixteenth. The fifth will have one thirty-second from the original mamzer. The sixth will have one sixty-fourth. The seventh generation will only have one out of one hundred and twenty-eight. The eighth will have one out of two hundred and fifty-six. The ninth will have one out of five hundred and twelve. The tenth generation will only have one out of one thousand and twenty-four from the original mamzer.

The portion of the mamzer that exists in the tenth-generation descendant has now become nullified. The Yerushalmi states that a berya, a complete creature can become nullified if it is intermingled among a mixture of more that nine hundred and sixty.

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Is that true Lhalcha they can now marry into Klal yisroel? –  YUASK Aug 18 '13 at 22:33
    
This is cute, but in addition to YUASK's point, who is marrying the mamzer the first 9 times? What if two of the ancestors are mamzerim? –  Double AA Aug 18 '13 at 23:57
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@doubleaa A Mamzer can marry a convert or descendant of converts. The child is still a Mamzer. Rambam issurrei biah 15:7-8 m.chabad.org/library/article_cdo/aid/960663/jewish/… –  Menachem Aug 19 '13 at 1:14
    
"The child is still a mamzer" Correct. So how can you get 10 generations removed? Are you suggesting he's really half a mamzer? What about the fact that Birya not being batel is only derabanan? –  Double AA Aug 19 '13 at 1:26
    
But he's only a Mamzer because his fathers a Mamzer not because he is the fruit of a forbidden relationship. that is what the gra is saying. Note that I haven't seen the gra inside and don't think he holds that a Mamzer is muttar after 10 generations. I think he is just explaining why it says 10. And perhaps why reish lakesh say he is muttar after 10 generations. @double –  Menachem Aug 19 '13 at 1:31

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