OnlineWoerterBuecher.de
Internes

Lexikon


aleph 0


The href="module.php?name=Lexikon&file=search&eid=1&query=cardinality">cardinality of the first href="module.php?name=Lexikon&file=search&eid=1&query=infinite">infinite href="module.php?name=Lexikon&file=search&eid=1&query=ordinal">ordinal, href="module.php?name=Lexikon&file=search&eid=1&query=omega">omega (the number of href="module.php?name=Lexikon&file=search&eid=1&query=natural numbers">natural numbers). Aleph 1 is the cardinality of the smallest href="module.php?name=Lexikon&file=search&eid=1&query=ordinal">ordinal whose cardinality is greater than aleph 0, and so on up to aleph omega and beyond. These are all kinds of href="module.php?name=Lexikon&file=search&eid=1&query=infinity">infinity. The href="module.php?name=Lexikon&file=search&eid=1&query=Axiom of Choice">Axiom of Choice (AC) implies that every set can be href="module.php?name=Lexikon&file=search&eid=1&query=well-ordered">well-ordered, so every href="module.php?name=Lexikon&file=search&eid=1&query=infinite">infinite href="module.php?name=Lexikon&file=search&eid=1&query=cardinality">cardinality is an aleph but in the absence of AC there may be sets that can' t be well-ordered (don' t posses a href="module.php?name=Lexikon&file=search&eid=1&query=bijection">bijection with any href="module.php?name=Lexikon&file=search&eid=1&query=ordinal">ordinal) and therefore have cardinality which is not an aleph. These sets don' t in some way sit between two alephs they just float around in an annoying way, and can' t be compared to the alephs at all. No href="module.php?name=Lexikon&file=search&eid=1&query=ordinal">ordinal possesses a href="module.php?name=Lexikon&file=search&eid=1&query=surjection">surjection onto such a set, but it doesn' t surject onto any sufficiently large ordinal either. (1995-03-29)

In addition suitable contents:
[ href="module.php?name=Lexikon&op=content&tid=31">2 ] [ href="module.php?name=Lexikon&op=content&tid=134">= ] [ href="module.php?name=Lexikon&op=content&tid=433">al ] [ href="module.php?name=Lexikon&op=content&tid=457">Aleph ] [ href="module.php?name=Lexikon&op=content&tid=544">am ] [ href="module.php?name=Lexikon&op=content&tid=592">an ] [ href="module.php?name=Lexikon&op=content&tid=740">ar ] [ href="module.php?name=Lexikon&op=content&tid=743">arc ] [ href="module.php?name=Lexikon&op=content&tid=759">arg ] [ href="module.php?name=Lexikon&op=content&tid=894">at ] [ href="module.php?name=Lexikon&op=content&tid=996">av ] [ href="module.php?name=Lexikon&op=content&tid=1018">Axiom of Choice ] [ href="module.php?name=Lexikon&op=content&tid=1026">b ] [ href="module.php?name=Lexikon&op=content&tid=1181">be ] [ href="module.php?name=Lexikon&op=content&tid=1269">bi ] [ href="module.php?name=Lexikon&op=content&tid=1294">bijection ] [ href="module.php?name=Lexikon&op=content&tid=1606">bs ] [ href="module.php?name=Lexikon&op=content&tid=1708">C ] [ href="module.php?name=Lexikon&op=content&tid=1724">ca ] [ href="module.php?name=Lexikon&op=content&tid=1818">card ] [ href="module.php?name=Lexikon&op=content&tid=1821">cardinality ] [ href="module.php?name=Lexikon&op=content&tid=2000">Ch ] [ href="module.php?name=Lexikon&op=content&tid=2001">ch ] [ href="module.php?name=Lexikon&op=content&tid=2099">ci ] [ href="module.php?name=Lexikon&op=content&tid=2247">co ] [ href="module.php?name=Lexikon&op=content&tid=2330">com ] [ href="module.php?name=Lexikon&op=content&tid=3151">de ] [ href="module.php?name=Lexikon&op=content&tid=3565">do ] [ href="module.php?name=Lexikon&op=content&tid=3752">du ] [ href="module.php?name=Lexikon&op=content&tid=3865">ec ] [ href="module.php?name=Lexikon&op=content&tid=3896">ed ] [ href="module.php?name=Lexikon&op=content&tid=3929">ee ] [ href="module.php?name=Lexikon&op=content&tid=3946">eg ] [ href="module.php?name=Lexikon&op=content&tid=4148">er ] [ href="module.php?name=Lexikon&op=content&tid=4171">es ] [ href="module.php?name=Lexikon&op=content&tid=4199">et ] [ href="module.php?name=Lexikon&op=content&tid=4497">fi ] [ href="module.php?name=Lexikon&op=content&tid=4520">file ] [ href="module.php?name=Lexikon&op=content&tid=4559">finite ] [ href="module.php?name=Lexikon&op=content&tid=4700">fo ] [ href="module.php?name=Lexikon&op=content&tid=4727">for ] [ href="module.php?name=Lexikon&op=content&tid=4989">ga ] [ href="module.php?name=Lexikon&op=content&tid=5057">ge ] [ href="module.php?name=Lexikon&op=content&tid=5291">gr ] [ href="module.php?name=Lexikon&op=content&tid=5339">greater than ] [ href="module.php?name=Lexikon&op=content&tid=5434">h ] [ href="module.php?name=Lexikon&op=content&tid=5540">hat ] [ href="module.php?name=Lexikon&op=content&tid=5722">hose ] [ href="module.php?name=Lexikon&op=content&tid=5768">hr ] [ href="module.php?name=Lexikon&op=content&tid=5769">hs ] [ href="module.php?name=Lexikon&op=content&tid=5931">id ] [ href="module.php?name=Lexikon&op=content&tid=5956">ie ] [ href="module.php?name=Lexikon&op=content&tid=6013">il ] [ href="module.php?name=Lexikon&op=content&tid=6052">implies ] [ href="module.php?name=Lexikon&op=content&tid=6064">in ] [ href="module.php?name=Lexikon&op=content&tid=6103">infinite ] [ href="module.php?name=Lexikon&op=content&tid=6108">infinity ] [ href="module.php?name=Lexikon&op=content&tid=6413">io ] [ href="module.php?name=Lexikon&op=content&tid=6449">ir ] [ href="module.php?name=Lexikon&op=content&tid=6482">is ] [ href="module.php?name=Lexikon&op=content&tid=6558">it ] [ href="module.php?name=Lexikon&op=content&tid=6822">ki ] [ href="module.php?name=Lexikon&op=content&tid=6918">la ] [ href="module.php?name=Lexikon&op=content&tid=7091">Lex ] [ href="module.php?name=Lexikon&op=content&tid=7107">li ] [ href="module.php?name=Lexikon&op=content&tid=7441">ly ] [ href="module.php?name=Lexikon&op=content&tid=7463">ma ] [ href="module.php?name=Lexikon&op=content&tid=7579">mall ] [ href="module.php?name=Lexikon&op=content&tid=7721">meg ] [ href="module.php?name=Lexikon&op=content&tid=8032">mo ] [ href="module.php?name=Lexikon&op=content&tid=8040">mod ] [ href="module.php?name=Lexikon&op=content&tid=8079">module ] [ href="module.php?name=Lexikon&op=content&tid=8167">mp ] [ href="module.php?name=Lexikon&op=content&tid=8384">N ] [ href="module.php?name=Lexikon&op=content&tid=8386">na ] [ href="module.php?name=Lexikon&op=content&tid=8449">natural number ] [ href="module.php?name=Lexikon&op=content&tid=8460">nc ] [ href="module.php?name=Lexikon&op=content&tid=8622">nf ] [ href="module.php?name=Lexikon&op=content&tid=8627">ng ] [ href="module.php?name=Lexikon&op=content&tid=8630">ni ] [ href="module.php?name=Lexikon&op=content&tid=8672">nn ] [ href="module.php?name=Lexikon&op=content&tid=8675">no ] [ href="module.php?name=Lexikon&op=content&tid=8787">nu ] [ href="module.php?name=Lexikon&op=content&tid=8799">numbers ] [ href="module.php?name=Lexikon&op=content&tid=8964">om ] [ href="module.php?name=Lexikon&op=content&tid=8997">onto ] [ href="module.php?name=Lexikon&op=content&tid=9116">ordinal ] [ href="module.php?name=Lexikon&op=content&tid=9204">pa ] [ href="module.php?name=Lexikon&op=content&tid=9550">ph ] [ href="module.php?name=Lexikon&op=content&tid=9651">pl ] [ href="module.php?name=Lexikon&op=content&tid=10253">query ] [ href="module.php?name=Lexikon&op=content&tid=10364">rc ] [ href="module.php?name=Lexikon&op=content&tid=10385">re ] [ href="module.php?name=Lexikon&op=content&tid=10767">ro ] [ href="module.php?name=Lexikon&op=content&tid=11150">se ] [ href="module.php?name=Lexikon&op=content&tid=11281">set ] [ href="module.php?name=Lexikon&op=content&tid=11376">si ] [ href="module.php?name=Lexikon&op=content&tid=11506">sit ] [ href="module.php?name=Lexikon&op=content&tid=11556">sm ] [ href="module.php?name=Lexikon&op=content&tid=11615">sn ] [ href="module.php?name=Lexikon&op=content&tid=11651">so ] [ href="module.php?name=Lexikon&op=content&tid=11934">st ] [ href="module.php?name=Lexikon&op=content&tid=12133">su ] [ href="module.php?name=Lexikon&op=content&tid=12211">surjection ] [ href="module.php?name=Lexikon&op=content&tid=12359">T ] [ href="module.php?name=Lexikon&op=content&tid=12588">th ] [ href="module.php?name=Lexikon&op=content&tid=12721">to ] [ href="module.php?name=Lexikon&op=content&tid=12939">tw ] [ href="module.php?name=Lexikon&op=content&tid=13030">um ] [ href="module.php?name=Lexikon&op=content&tid=13146">up ] [ href="module.php?name=Lexikon&op=content&tid=13175">us ] [ href="module.php?name=Lexikon&op=content&tid=13310">ve ]






Go Back ]

Free On-line Dictionary of Computing

Copyright © by OnlineWoerterBuecher.de - (5832 Reads)

All logos and trademarks in this site are property of their respective owner.

Page Generation in 0.0973 Seconds, with 16 Database-Queries
Zurück zur Startseite