Revision #792 → #1229 · back to history
addedFloor function0896cfc66dd2
addedCeiling function299780286850
addedFloor and ceiling of ±2.4e4005b8d15fa
addedFloor and ceiling agree on integersa640ab70f9ac
addedfloor(x+1) vs ceil(x) at integersc6d5e81e8594
addedFractional part83f8c1d10e49
addedBounds on fractional partd961cacac443
addedFloor and ceiling via defining equations5d0ac7ab5dcc
addedUnique integers in half-open interval55b15297e794
addedEquivalence formulas for floor/ceiling166c0fa39986
addedFloor as residuated mapping / Galois connection20d7fb834273
addedAdding an integer to the argument1824663e3373
addedInequalities for non-integer shifts2a30a5610b3e
addedMonotonicity of floor and ceilingc24e9eeba506
addedFloor ≤ ceiling, equality iff integer3d9da6b492d7
addedFloor and ceiling are identity on integers2d3ac4fcede1
addedNegation swaps floor and ceiling8420130a9ad8
addedNegation complements fractional part45791a95fcb9
addedIdempotence of floor, ceiling, fractional parta8beb369bc9c
addedNested floor/ceiling collapse to innermost7cdec9c4cfca
addedInteger quotient floor identity9c9813a6aaa8
addedIdentity for positive n0cd22f40d8eb
addedIdentity for positive m053c7a284d73
addedCase m = 2122b89dac3a4
addedHermite's identity13cb2101221c
addedConverting floors to ceilings7f60a9db6182
addedIdentity for strictly positive integers3005f41704ee
addedReduction for coprime m and nbf45c3d5aa86
addedCoprime ceiling and fractional part identitiesddf10a248899
addedSymmetry implication1acade3b733c
addedReciprocity law for positive m, n12bc8824cb1b
addedDivision by positive integers property81a8dca1a7b3
addedRemainder identity for d positive integerd7c676092d71
addedNested divisions identity9fc07edabb0a
addedDiscontinuity and semi-continuity9d169edc5afd
addedUpper/lower semi-continuity50806370ddb1
addedFourier series of fractional partfadfe86005e3
addedConvergence at discontinuitiescc7b3611afbb
addedFloor Fourier expressionda3a8cd5474d
addedModulo operation extended to realsedebd5f22ccf
addedx mod y bounded by y3730609a1384
addedQuadratic reciprocity via floor4154851b0bb1
addedFloor formulas for quadratic charactera3d687ad1e7b
addedRounding to nearest integer (ties up)034d4702527e
addedRounding towards negative infinity842c0e91ac58
addedRounding away from 03c52fc66d42d
addedRounding towards evenc746d9786733
addedUniform quantizer4f21592047d9
addedNumber of digits in base bdbbf22a53904
addedNumber of strings without repeated charactersac86157ec9c9
addedn = 26 alphabet countebf4214430a5
addedLegendre's formula for factorialsc56941dcecea
addedBeatty sequence partition57f19aff5d57
addedFormulas for Euler's constant1f0b3346cd3a
addedIntegral identity for continuous derivativef813fcb3c5f8
addedZeta function representation5b02ecbe0bfd
addedValidity and extension of zeta formulaf7352736efa1
addedZeta in critical strip5f916eb2dfff
addedPrimality test via floorf9782fb40506
addedFormula for n-th prime via αd52123056600
addedMills' constantbec810db8f30
addedNumber ω generating primesb2ed7b0c74c5
addedPrime counting via Wilson's theorem25ca8fe9dc1c
addedPrime counting formula for n ≥ 24961282dc5e0
addedRamanujan's floor function problems6bff973ea0a2
addedWaring's problem unsolved floor identityd66506238508
addedMahler finiteness result2c37c98ce5f5
addedArithmetic right-shift equals floor division5e1d0dfb31d9