Revision #498 → #1056 · back to history
addedCardinal number39aaf9dff921
addedSame cardinality (bijection)3392378fc19a
addedNaturals and rationals equinumerous325b326ac3d4
addedCantor: infinite sets can differ in cardinality894704da55ec
addedAleph-null as smallest alephb1eb77064f76
addedSameness of cardinality is an equivalence relationfd539b947539
addedEquivalence class corresponds to a cardinal02cdcc92405a
addedHilbert's Grand Hotel bijection0c49fac822eb
addedPlus-one need not give a new cardinal2b9d921a2367
addedPower set gives strictly greater cardinality3d8b3109822e
addedMore reals than naturals3c4163d17a2d
addedCardinality function4907f8b8c7c0
addedAxiom of cardinality / Hume's principle875c19c69ada
addedWeak cardinal assignment (Moschovakis)57a20fb97d4b
addedStrong cardinal assignment67d0386c5aad
addedVon Neumann cardinal assignment68f900589467
addedInitial ordinalab56a66cce67
addedAll finite ordinals are initial ordinals067ea83f6aa6
addedMany infinite ordinals share a cardinalityaca07ba9f55d
addedAleph number notation75eab9eed6b7
addedSmallest uncountable ordinal0cea53b37196
addedInfinite initial ordinals are limit ordinalsc04d18548325
addedCardinality as class of equinumerous setsc73ff076cbc6
added[X] is a proper class0690d7101eb5
addedScott's trick (least rank)100e10bcc1e2
addedLévy mixed cardinal definitiona926d8643d5b
addedOrder on cardinals93bd4d647090
addedCantor–Bernstein–Schroeder theorem7a3362ea5b16
addedAC equivalent to cardinal comparability5635d80b27cd
addedDedekind-infinite / Dedekind-finite149c2b353be8
addedFinite cardinals are the natural numbersfb348904b573
addedDedekind-infinite implies infinite4950c14eb97b
addedDedekind notions match standard under ACcb190403dfb3
addedAleph numbersaaa575c109c4
addedAn aleph for every ordinal730837b76183
addedUnder AC all infinite cardinals are alephs030e34de1b53
addedNon-aleph cardinals incomparable (Hartogs)d2a7b13fab00
addedFinite cardinal arithmetic agrees with naturals70056af041fa
addedSuccessor cardinalb4bfc8f5e49f
addedMinimal successor cardinal without AC (Hartogs)6b3064791dc0
addedCardinal addition via disjoint union47e95936d1dd
addedZero is additive identity66ca874e697d
addedAddition is associativefdb9318f9689
addedAddition is commutative33427461a02d
addedAddition is non-decreasingedf5805607e8
addedInfinite cardinal addition under AC972b7c6ffeed
addedCardinal subtractiond9e7f14aeded
addedCardinal multiplication via Cartesian product8b6884023ed6
addedZero is multiplicative absorbing element200a08c0a52e
addedNo nontrivial zero divisorsae559568ae42
addedOne is multiplicative identityb1d72153d6de
addedMultiplication is associative941e6c055346
addedMultiplication is commutative1ea57e4ccd28
addedMultiplication is non-decreasingdd58b22b960c
addedMultiplication distributes over addition6752986d56de
addedInfinite cardinal multiplication under AC057f2d29755e
addedInfinite product equals sum4fecd85e71ac
addedCardinal division618a9afca3ea
addedCardinal exponentiation via function space9139a3d36b75
addedκ^0 = 1 (empty function)85ce459b73ae
added0^μ = 0 for μ ≥ 1bff8c880daf9
addedExponent addition lawac86e407a239
addedExponent multiplication law979d5d19a999
addedProduct raised to a powerf10830df930a
addedExponentiation is non-decreasing4bf31f570b2b
addedCantor: 2^|X| > |X|7ae254e375d7
addedNo largest cardinal35e974e6e357
addedCardinals form a proper class2d3b6b86e640
addedFinite bases, infinite exponent equal7d7ee320302f
addedInfinite base, finite exponentf3b9c4b11391
addedBounds on κ^μcd525f80d235
addedKőnig's theorem inequalities2e445c07bcc2
addedCardinal roots7f974a3cabaf
addedExistence of cardinal logarithm2a6ba8635cc8
addedLogarithm of an infinite cardinal04498860afe1
addedContinuum hypothesisc23fb1d16b64
addedGeneralized continuum hypothesis86d5f61b2f39
addedCH and GCH independent of ZFCe59aa58cbcf4
addedEaston's theoreme2b377ef2c8f
addedFinite sets: bijection iff equal count9aefc41e22db
addedDenumerable (countably infinite) sets0a1577c8bedf
addedTransfinite cardinal numbers59a6f585b923
addedUnbounded subset of N equinumerous with N8120620efe73
addedOrdered pairs of naturals are denumerabled0a1bfdab9b0
addedReal algebraic numbers are denumerabled00eb6d28c89
addedReals exceed naturals in cardinalityf80deaa9f951
addedSmallest transfinite cardinal and successors7fb0615f8e1e
addedGödel and Cohen: independence of CH1a550e8f1f5b