Bilangan kardinal: Perbedaan antara revisi

== Definisi formal ==

Secara formal, urutan di antara bilangan kardinal didefinisikan sebagai berikut: |''X''| ≤ |''Y''| berarti bahwa ada fungsi [[injektif]] dari ''X'' ke ''Y''. [[Teorema Cantor–Bernstein–Schroeder]] menyatakan jika |''X''| ≤ |''Y''| dan |''Y''| ≤ |''X''| maka |''X''| = |''Y''|. [[Aksioma pilihan]] setara dengan pernyataan yang diberikan dua set ''X'' dan ''Y'', baik |''X''| ≤ |''Y''| maupun |''Y''| ≤ |''X''|.<ref name="Enderton">Enderton, Herbert. "Elements of Set Theory", Academic Press Inc., 1977. {{ISBN|0-12-238440-7}}</ref><ref>{{citation | author=[[Friedrich M. Hartogs]] | editor=[[Felix Klein]] |editor2=[[Walther von Dyck]] |editor3=[[David Hilbert]] |editor4=[[Otto Blumenthal]] | title=Über das Problem der Wohlordnung | journal=Math. Ann. | volume=Bd.&nbsp;76 | number=4 | publisher=B.&nbsp;G. Teubner | location=Leipzig | year=1915 | pages=438–443 | issn=0025-5831 |url=http://gdz.sub.uni-goettingen.de/index.php?id=11&PPN=PPN235181684_0076&DMDID=DMDLOG_0037&L=1 | doi=10.1007/bf01458215}}</ref>

 

== Referensi ==

{{Reflist}}

== Pranala luar ==

* [http://www.apronus.com/provenmath/cardinality.htm Cardinality at ProvenMath] formal proofs of the basic theorems on cardinality.