Rebbe Chalaftah ben Dosa from Kfar Chanina says: Ten people who are sitting
and involved in Torah [study] have the Divine presence residing among
them, as it is written "G-d stands in a Divine gathering..."(Tehillim
82:1). What is the source that even among five people [His presence
resides]? As it is written "...and He established the foundation of His
group upon the earth" (Amos 9:6). What is the source that this is true
even among three people? As it is written "..in the presence of judges He
will judge" (Tehillim 82:1). What is the source that this is true even
among two? As it is written "Then those who fear G-d spoke to each other,
and G-d listened and heard..." (Malachi 3:16). What is the source that this
is true even of one [sitting and involved in Torah]? As it is written "In
every place that I allow my name to be mentioned, I will come to you and
bless you" (Shmoth 20:21).

A number of questions need to be asked. First, what is the significance
specifically of ten people? And what is the significance of exactly five?
Three? Secondly, if the Divine presence resides with even one person who is
involved in Torah study, what was the need for telling us two, three, five
and ten!? Another question is why the verse "Let him sit in solitude and
be still, for he has taken it upon himself" was not used as the proof text
for one person involved in Torah study, since it was used by Rebbe Chanania
ben Tradyon (Ch. 3, Mishna 3). The Tanna used the same verse as Rebbe
Chanania ben Tradyon for two people, so why did he bring a different verse
for one person? Finally, what proof is being brought from the verse "and
founded his group (agudato) on the earth," which has no mention of any
number in it?

It is known that the number ten is called an "eidah", which refers to the
"klal" (comprehensive, all-inclusive). Neither an eidah nor a klal can be
less than ten.. This can be seen from the structure of the numbers. No
number goes beyond ten, for at that point, the counting begins again at
one. Every number below ten is viewed as incomplete, since we can add to
it, and reach a higher number. Ten represents completeness, since we don't
go higher than ten, but rather we start over again. (Twelve is ten and
another two; thirty seven is three tens and another seven. Two hundred
seventy five is two groups of ten tens, another seven tens, and an
additional five.) This will be further explained in the fifth chapter

(The opening Mishnayot of that chapter inform us that there were ten
statements of creation, ten generations from Adam to Noach and ten from
Noach to Avaraham, ten tests of Avraham, ten miracles at the exodus from
Egypt and another ten at the Red Sea, ten plagues visited upon the
Egyptians, ten tests of the Jews in the desert, ten daily miracles in the
Holy Temple, and ten things created at twilight before Shabbat. It is not
coincidental that each of the above were ten, and the Maharal will
elaborate on this in his commentary there.)

(The significance of ten as the number that gathers together all the "ones"
that come before and represents them in a new column reflects something
fundamental about the number ten. In addition, the fact that we use a base
10 for our mathematics, rather than a different base, is not viewed as
simply functional. "Hey, we have ten fingers and ten toes." Nor that base
10 simply lets us minimize the number of places we need to use for larger
numbers, since in a base 8, the number 83 would have to be written as 123,
and in a base 2, it would stretch to 1,010,011 . Using 10 as our base is
fundamental, based on the inner meaning of each number. The Pesach song
"Echad mi yodeiah" is a Kabbalistic presentation of the inner meaning of
each number. In fact, even in other bases, we see that the number 10
represents the completion of the base. With all the units being grouped
together, whether it is a base of two, eight or ten, the 1 of the 10
represents that group, with the counting process beginning over again,.)

Since every number until ten is viewed as incomplete, and the number ten
represents completeness, G-d's presence resides among ten, and no activity
of sanctification can take place with less than ten. (See Brachoth 21b, and
Shulchan Aruch Orach Chaim 55.)