Revision #180 → #1317 · back to history
addedNegative integers9fbc4c0d601b
addedChain of subsets N ⊂ Z ⊂ Q ⊂ Ra6e8c9a2c2be
addedZ is countably infinitec76594faa8ef
addedInteger as real without fractional component4f95d5effcaa
addedIntegers vs non-integers693bb3a29e15
addedSmallest group and ring containing Nd5d90e3a39ec
addedRational integersa3e79bed6f2d
addedRational integers are rational algebraic integers107dcd10d4a5
addedClosed under addition and multiplication13bcb6aee900
addedClosed under subtraction180d37b841ed
addedZ is initial object in category of rings420ad613f100
addedInjectivity iff characteristic zero4f87b71d655a
addedCharacteristic-zero rings contain a copy of Z61b97d93ee7b
addedNot closed under division945f3961885d
addedNot closed under exponentiation73a76f315f32
addedZ under addition is an abelian groupbf4134238083
addedZ under addition is cyclicd4ad90eb4894
addedZ is the unique infinite cyclic group978abcebb3b2
addedZ under multiplication is a commutative monoida2ffff09d094
addedZ under multiplication is not a groupd5e444c10f1b
addedZ is a commutative ring with unity20808e053816
addedZ is an integral domaina2bdcf00bfd8
addedZ is not a field290f50f18296
addedSmallest field containing Z is Q0b599be8329a
addedEuclidean division91419468d133
addedZ is a Euclidean domain (hence PID)6b24a6f7e3e3
addedFundamental theorem of arithmetic8a1d3d03117d
addedZ is totally ordered without boundsfd206e3d4ff8
addedPositive and negative integersa68d34f6fce4
addedOrder compatible with operationsf7709ae92c47
addedZ is an ordered ringbc5e3ee1d11b
addedZ characterized as well-ordered ordered abelian group571efcedf168
addedTraditional construction of integers94c2eb09c4c2
addedPiecewise arithmetic operationsf7d237ef3af1
addedIntegers as equivalence classes of pairs7fa46cfedbf1
addedEquivalence relation on pairsca94de0d4cb4
addedAddition and multiplication of classesaab96ede2c7e
addedNegation of a class3cdc62fe4492
addedSubtraction via additive inverse2a86e21d4320
addedStandard ordering on classesacf49cc645b9
addedCanonical representative of each class613a609a70cd
addedExamples of class arithmetic3828cd9af5fe
addedMultiple constructions of signed integers50683c470b9b
addedZ is countably infinite224b18c23c11
addedPairing of integers with naturalsad98172d24eb
addedCardinality of Z is aleph-null6ee72ea22d91
addedBijectionb9a6e98653fd