Revision #225 → #1422 · back to history
addedNatural number0c47a7a5170f
addedCardinal numbera6e56947ad6b
addedOrdinal number77c058782bab
addedNominal number954407f00a28
addedCardinality4e8d256ce77f
addedEqual cardinality via one-to-one correspondenceb0bed557c15a
addedSize relationship between collections25df4598487c
addedSequence5713b8514aa0
addedOrder typece24fa9ee7ad
addedNatural numbers as simplest infinite well-ordered sete3aa47f582f1
addedTwo definitions of natural numbers2d206d429001
addedPositive integers and non-negative integers4008894646cc
addedWhole numbersd0a03cd8886c
addedDecimal system5c0ec7ee1e19
addedCounting3c2605ac57fb
addedCardinality principled1c6dc8e8db9
addedSuccessore4ad574b1661
addedPeano axioms66ff56e95c78
addedAxiom of induction247dd6470b21
addedvon Neumann ordinals constructiond60187eb216a
addedSet-theoretic cardinalityeb22bb2cd572
addedSet-theoretic order05053ae4f77c
addedZermelo ordinals2021d5249bdc
addedDefinition of addition1997e851542e
addedAddition as repeated application of successoraddd02ad7300
added(ℕ, +) is a commutative monoid673d96e46bef
added(ℕ, +) is a free monoid on one generator4e3076feef0e
addedCancellation property and embedding in a groupd400996b07e7
addedSmallest group containing ℕ is the integers23c2cdde0022
addedDefinition of multiplicationd200df2dd535
added(ℕ, ×) is a free commutative monoidc3a4cbd3b488
addedPrimes generate the multiplicative monoidb7fe22146a06
addedDistributive lawcf906710e986
addedℕ not closed under subtraction90bd6449b078
addedℕ is a semiring, not a ringd7d769d0d38e
addedℕ excluding 0 has no identity element4d201311ff76
addedTotal order on natural numberse14783262d73
addedOrder compatible with operations35215f52b8a7
addedWell-ordering of the natural numbers136eec5fa9c9
addedEuclidean division7e2648b95707
addedQuotient and remainderc06663e15cce
addedUniqueness of quotient and remainder1fe8b46fc77a
addedClosure under addition and multiplicationfe6a940d5c9f
addedAssociativity34125a4c855b
addedCommutativityc2d4a649c72d
addedExistence of identity elements77a11cd87a90
addedDistributivity of multiplication over addition0ec506eb3394
addedNo nonzero zero divisors08a3ac9c7eff
addedConstruction of the integersfa537d3cdcb8
addedConstruction of the rational numbers6750771620fc
addedConstruction of the real numbers0bafe3046f1e
addedConstruction of the complex numbersc89541ca8a40