The Continuum
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In our eReader you can find the full English version of the book. Read The Continuum Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book The Continuum
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(6) A series may be dense and closed and not be dense-in-itself, * as for example the series F + + *F, where V denotes, for the moment, Veblen's series described in § 64, 3, b, and *V the same series in reverse order. Here the element is not the limit of any fundamental sequence, since every progression in V has a limit in V, and every regression in *F has a limit in *V, if we admit the valid- ity of Cantor's reasoning in regard to the transfinite well-ordered series (§ 83).
(7) A series may be... perfect (that is, dense-in-itself and closed), and yet have no last element and no first element, as for example the series *V + V. Here V and *V have the meanings just explained. !
By the aid of these definitions, Cantor defines a series of type 6 by the following two conditions: (A) the series must he perfect (that is, dense-in-itself and closed); and (B) the series w, ust contain a denumerable subclass R in such a way that between any two elements of the given series there is an ele- ment of R.
What to read after The Continuum?
You can find similar books in the "Read Also" column, or choose other free books by E V Edward Vermilye Huntington to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
(6) A series may be dense and closed and not be dense-in-itself, * as for example the series F + + *F, where V denotes, for the moment, Veblen's series described in § 64, 3, b, and *V the same series in reverse order. Here the element is not the limit of any fundamental sequence, since every progression in V has a limit in V, and every regression in *F has a limit in *V, if we admit the valid- ity of Cantor's reasoning in regard to the transfinite well-ordered series (§ 83).
(7) A series may be... perfect (that is, dense-in-itself and closed), and yet have no last element and no first element, as for example the series *V + V. Here V and *V have the meanings just explained. !
By the aid of these definitions, Cantor defines a series of type 6 by the following two conditions: (A) the series must he perfect (that is, dense-in-itself and closed); and (B) the series w, ust contain a denumerable subclass R in such a way that between any two elements of the given series there is an ele- ment of R.
What to read after The Continuum?
You can find similar books in the "Read Also" column, or choose other free books by E V Edward Vermilye Huntington to read onlineMoreLess
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