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critic
Tosafot (D"H ka'an bzman hazeh) learns that since we make the laws of Shabbat in sync with what was done in the desert, we therefore consider a r'shut harabim to mean that you need 600,000 people going through that area.

A question that I had was that in reality, there were a lot more than 600,000 people if you include the women and children whom were not included in that count. I've heard that it was really closer to two million people. So why do we say that r'shut harabim means 600,000 people and not a higher number, such as 2 million? One of the answers we came up with is that the only definitive number we have of bnai yisrael in the desert is 600,000. There is no place that says an exact number including women and children. Because of that, we take the one definitive number that we DO have, and therefore come up with that number.

Another question I had that I did not get an answer for is exactly what number do we need to get r'shut harabim. Do we need 600,000 even, or does it have to be the actual number that is listed in the chumash? (I don't have one if front of me but IIRC, it was 603,000)
shim
The 603,000 iirc correctly included Levi'im of age, who did not participate in the army.

In any case, the number 600,000 is a round number used perhaps in the same way that the 70 who went down to Mitzrayim is. The list of 70 doesn't mention any women besides, I think, Serach bat Asher and Yocheved. Its patently obvious that the number 70 is given because it represents something rather than that there were only 70 people. There had to have been at least twice that many; in reality many more times than that if you take into account wives, daughters, concubines, slaves etc. In a similar fashion, the number 600,000 always represents the benei yisrael in the midbar. Numbers like 2 million, although obvious if you consider average population distributions, basically only come up when people are discussing the historicity of it; the number of witnesses at Har Sinai etc.
Chai18
I think that it is not so much the actual number that is so important, it is the idea. while we can use 600,000 as the basic requirement for what constitutes a r'shut harabim, i think the number is more just to represent how you need a significant number of people to create a r'shut harabim and thus the 600,000 is used for the reasons explained by tosfot.
quark
QUOTE(critic @ May 9 2005, 09:09 AM)
Tosafot (D"H ka'an bzman hazeh) learns that since we make the laws of Shabbat in sync with what was done in the desert, we therefore consider a r'shut harabim to mean that you need 600,000 people going through that area.

A question that I had was that in reality, there were a lot more than 600,000 people if you include the women and children whom were not included in that count.  I've heard that it was really closer to two million people.  So why do we say that r'shut harabim means 600,000 people and not a higher number, such as 2 million?  One of the answers we came up with is that the only definitive number we have of bnai yisrael in the desert is 600,000.  There is no place that says an exact number including women and children.  Because of that, we take the one definitive number that we DO have, and therefore come up with that number.

Another question I had that I did not get an answer for is exactly what number do we need to get r'shut harabim.  Do we need 600,000 even, or does it have to be the actual number that is listed in the chumash? (I don't have one if front of me but IIRC, it was 603,000)
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Tosefos in Euvin 6a asks your question and answers similarly but different that we determine the amount by the amount of people that are mentioned in the Toragh in the degolim which shows it to be sufficient to considerf it reshus harabim.

(i beleive if am not mistaking that Rishonim discuss this question).
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