Numerus realis

Multi tool use
Multi tool use














Systemata Numerica Mathematicae

Numeri Elementarii

Naturales N{displaystyle mathbb {N} } {0,1,2,3,...} sive {1,2,3,...}




  • Primi P{displaystyle mathbb {P} } {2,3,5,7,11,...}


  • Abundantes

  • Amicabiles

  • Compositi

  • Defectivi

  • Perfecti


  • Sociabiles



Integri Z{displaystyle mathbb {Z} } {...,-2,-1,0,+1,+2,...}




  • Pares {...,-2,0,+2,...}


  • Impares {...,-3,-1,+1,+3,...}



Rationales Q{displaystyle mathbb {Q} }
Reales R{displaystyle mathbb {R} }




  • Irrationales



  • Algebraici



  • Transcendentes


    • Numerus pi π≈3.14159265358979…{displaystyle pi approx 3.14159265358979ldots }



    • Numerus Euleri e≈2.718281828459045…{displaystyle eapprox 2.718281828459045ldots }




Complexi C{displaystyle mathbb {C} }




  • Numerus imaginarius i=−1{displaystyle i={sqrt {-1}}}



  • Quaterni H{displaystyle mathbb {H} }


  • Octoni O{displaystyle mathbb {O} }


Infinitas ∞{displaystyle infty }



Variae radices


  • Radix binaria(2)

  • Radix octalis(8)

  • Radix decimalis(10)

  • Radix sedecimalis(16)



Numerus realis[1] est numerus ullus qui punctis decimalibus infinitis scribatur, sicut 9.73985647892038457. . . . Includuntur numeri rationales sicut 42 et −23/129, et irrationales sicut π et radices quadratae.




Linea numerorum


Puncta lineae infinitae numeros reales repraesentant: numeri positivi ad dexteram partem, negativi ad sinistram; numeri quorum magnitudo maior sit longior absunt ab puncto quod zero repraesentat.


Numeri integri (... -3, -2, -1, 0, 1, 2, 3, ...) punctis repraesentantur quae intervallis aequis inter se distant. Numeri rationales inter puncta integralia sunt; tanti rationales sunt quanti sunt integri. Plures autem numeri irrationales sunt quam rationales.




Numerus irrationalis 2{displaystyle {sqrt {2}}} inter duas copias rationalium. Numeri rubri quadratum < 2 habent; numeri caeruli quadratum > 2 habent.


Numeri rationales sunt rationes vel fractiones. Numeri irrationales (per definitionem) non sunt. Definitio numeri cuiusdam irrationalis est limes sequentiae numerorum rationalium; haec est repraesentatio decimalis. Definitio analytica sectione Dedekind utitur. Sectio Dedekind numeri realis X est divisio numerorum rationalium in duas partes, quarum una, pars sinistra, omnes numeros < X continet, altera, pars dextra, omnes numeros > X. Si X = 2{displaystyle {sqrt {2}}}, copia sinistra sectionis Dedekind X continet 1, 13/10, 239/169, 1393/185, etc. Copia dextra continet 3/2, 3363/2378, etc.



Notae |




  1. ↑ Renatus Cartesius, Geometria III p. 76. "Quemadmodum, tametsi tres imaginari possimus in hac, x3—6xx+13x—10 = 0; tamen una tantùm est realis; nempe 2; et quod ad reliquas duas attinet, quamvis illae augeantur, diminuantur, aut multiplicentur, sicut iam exposui; tamen non nisi imaginariae fieri possunt.



Nexus externi |




  • Numeri reales: Pythagoras ad Stevin (Anglice)


  • Numeri reales: Stevin ad Hilbertum (Anglice)


  • Numeri reales: Intellegere (Anglice)









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