Re: limits of finite sets

I asked for an explanation of the following result:

...

the limit in Set of any diagram

... ---> S_3 ---> S_2 ---> S_1

of finite nonempty sets is nonempty

a filtered inverse limit of finite sets is non empty this is frequently used without reference (eg, in SGA1 1960) for the case of finite groups (in fact it is not only non empty, but the projections are surjective, probably an equivalent statment) it is in Bourbaki, I think I can give a precise reference because I have already used it, but do not have it off mind now edubuc