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86 The elements of this aggregate are, therefore, the elements of $$M$$, of $$N$$, of $$P$$, $$...$$, taken together.

We will call by the name "part" or "partial aggregate" of an aggregate $$M$$ any other aggregate $$M_1$$ whose elements are also elements of $$M$$.

If $$M_2$$ is a part of $$M_1$$ and $$M_1$$ is a part of $$M$$, then $$M_2$$ is a part of $$M$$. Every aggregate $$M$$ has a definite "power," which we will also call its "cardinal number."

We will call by the name "power" or "cardinal number" of $$M$$ the general concept which, by means of our active faculty of thought, arises from the aggregate $$M$$ when we make abstraction of the nature of its various elements $$m$$ and of the order in which they are given.

[482] We denote the result of this double act of abstraction, the cardinal number or power of $$M$$, by (3) Since every single element $$m$$, if we abstract from its nature, becomes a "unit," the cardinal number $$\overline\overline{M}$$ is a definite aggregate composed of units, and this number has existence in our mind as an intellectual image or projection of the given aggregate $$M$$.

We say that two aggregates $$M$$ and $$N$$ are "equivalent," in signs (4) if it is possible to put them, by some law, in such a relation to one another that to every element of each one of them corresponds one and only one element