Bilangan kardinal: Perbedaan antara revisi
Konten dihapus Konten ditambahkan
k r2.5.4) (bot Menambah: ru:Кардинальное число |
Tidak ada ringkasan suntingan |
||
| (19 revisi perantara oleh 13 pengguna tidak ditampilkan) | |||
Baris 1:
'''Bilangan
Bilangan ini pertama kali ditemukan oleh [[Georg Cantor]] pada tahun [[1874]].
== Definisi formal ==
==Pranala luar==▼
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. 76 | number=4 | publisher=B. 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.apronus.com/provenmath/cardinality.htm Cardinality at ProvenMath] formal proofs of the basic theorems on cardinality.▼
*[http://www.math.cmu.edu/users/jcumming/teaching/undergraduate_set_theory_2009/Book.pdf Undergraduate Set Theory] more proofs about cardinality - includes proof of infinite cardinal addition in Section 4.2.▼
== Lihat pula ==
{{matematika-stub}}▼
* [[Bilangan ordinal]]
== Referensi ==
{{Reflist}}
▲== Pranala luar ==
▲* [http://www.apronus.com/provenmath/cardinality.htm Cardinality at ProvenMath] formal proofs of the basic theorems on cardinality.
▲* [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.
{{Sistem Bilangan}}
{{Teori himpunan}}
{{Authority control}}
[[Kategori:Bilangan]]
[[Kategori:Matematika]]
▲{{matematika-stub}}
[[ru:Кардинальное число]]
| |||