Bilangan kardinal: Perbedaan antara revisi

Formally,Secara theformal, orderurutan amongdi cardinalantara numbersbilangan iskardinal defineddidefinisikan assebagai followsberikut: |''X''| ≤ |''Y''| meansberarti thatbahwa thereada exists anfungsi [[injectiveinjektif]] function fromdari ''X'' toke ''Y''. The [[Teorema Cantor–Bernstein–Schroeder theorem]] statesmenyatakan that ifjika |''X''| ≤ |''Y''| anddan |''Y''| ≤ |''X''| thenmaka |''X''| = |''Y''|. The [[axiomAksioma of choicepilihan]] is equivalent tosetara thedengan statementpernyataan thatyang givendiberikan twodua setsset ''X'' anddan ''Y'', eitherbaik |''X''| ≤ |''Y''| ormaupun |''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>

* [http://www.math.cmu.edu/users/jcumming/teaching/undergraduate_set_theory_2009/Book.pdf Undergraduate Set Theory]{{Pranala mati|date=Februari 2021 |bot=InternetArchiveBot |fix-attempted=yes }} more proofs about cardinality - includes proof of infinite cardinal addition in Section 4.2.

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