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CONTRIBUTIONS TO THE FOUNDING OF THE THEORY OF TRANSFINITE NUMBERS
(First Article)
"Hypotheses non fingo."
"Neque enim leges intellectui aut rebus damus ad arbitrium nostrum, sed tanquam scribæ fideles ab ipsius naturæ voce latas et prolatas excipimus et describimus."
"Veniet tempus, quo ista quæ nunc latent, in lucem dies extrahat et longioris ævi diligentia."
§1
The Conception of Power or Cardinal Number
By an "aggregate" (Menge) we are to understand any collection into a whole (Zusammenfassung zu einem Ganzen) of definite and separate objects of our intuition or our thought. These objects are called the "elements" of .
In signs we express this thus:
(1)
.
We denote the uniting of many aggregates , , , , which have no common elements, into a single aggregate by
(2)
.
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