On a property of countable partitioning of the continuum without the use of Koenig's lemma
Without invoking Koenig's lemma or any other special results it is shown (based on some lemmas which may be of interest on their own) that if the set of all the real numbers is a union of countably many of its subsets then at least one of these subsets is of the power of the continuum.
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| Veröffentlicht in: | International journal of mathematical education in science and technology 1980-10, Vol.11 (4), p.475-478 |
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| Format: | Artikel |
| Sprache: | eng |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | Without invoking Koenig's lemma or any other special results it is shown (based on some lemmas which may be of interest on their own) that if the set of all the real numbers is a union of countably many of its subsets then at least one of these subsets is of the power of the continuum. |
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| ISSN: | 0020-739X 1464-5211 |
| DOI: | 10.1080/0020739800110402 |