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According to Numbers 34:5 the south-western most point of (Biblical) Israel is "Nachal Mitzrayim". My first question is what river is this referring to?

The first time I remember reading this I thought it was referring to the Nile River (or one of the tributaries that feed into it from the Mediterranean) because that seemed to be the main river in Egypt and it would make sense to refer to it as Nachal Mitzrayim. However on most of the maps that I saw of Biblical Israel, Nachal Mitzrayim is identified as Wadi El Arish (much closer to Israel). A related question can be seen here.

Who says that Nachal Mitzrayim is Wadi El Arish and why do they understand "Nachal Mitzrayim" this way?

My second question is: Does anyone say that Nachal Mitzrayim is the Nile?

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It doesn't make sense to be the Nile. The Nile was the middle of Egypt not its boundary. – Double AA Aug 8 '14 at 14:51
In modern Hebrew a river (like the Nile) is called Nahar (נהר), and Nachal (נחל) is used to describe smaller streams. Also, according to the Hebrew Wikipedia, in Biblical and Mishnaic Hebrew, a Nachal may refer also to a valley, even if no water flows through it. – Tamir Evan Aug 8 '14 at 14:53
@DoubleAA That's a good point, although if we were being given land that was already occupied by other nations maybe a (small) part of Mitzrayim would be given as well. In any event do we know that Mitzrayim's border ended with Nachal Mitzrayim? – Gavriel Aug 8 '14 at 14:56
@Gavriel Every border demarcates two countries. If it is our border it is also theirs. – Double AA Aug 8 '14 at 15:04

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