19/12/07 08:43:56.92 H2e5WMAT.net
>>617
つづき
For once 0 is a common element of all elements Z1 of T, and on the other hand, if a is a common element of all these Z1, then also {a} is common to all and therefore also an element of Z0.
If Z 'is any other quantity of the nature required in the axiom, then in the same way as Z0 it corresponds to Z for a smallest subset Z0' of the property under consideration.
Now, however, the average [Z0, Z0 '], which is a common subset of Z and Z', must have the same properties as Z and Z and, as a subset of Z, the constituent Z0 and, as a subset of Z ', the constituent Z0 ' contain.
After I it follows that [Z0, Z0 '] = Z0 = Z0', and that Z0 is therefore the common component of all possible quantities, such as Z, although these do not need to form the elements of a set.
The set Z0 contains the elements 0, {0}, {{0}}, and so on, and may be called a "series of numbers" because their elements can represent the location of the numerals.
It is the simplest example of a "countless infinite" set (Nos. 36).
注：36節(Nos. 36 P280)で、ZERMELOは無限（"unendliche"）について論じている。
つづく