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)









tAnPA cZPM4XXtI,Uz9
-
XnE0ZXT4

Popular posts from this blog

Tabula Rosettana

Image
Tabula multilinguis Rosettana in Museo Britannico ostenditur. Tabula Rosettana, [1] etiam titulo OGIS 90 agnita, est stela decreto de rebus sacris in Aegypto anno 196 a.C.n. lato inscripta. Tabula iuxta Rosettam Aegypti, urbem in delta Nili et ad oram maris Mediterranei iacentem, anno 1799 a milite Francico reperta est. Inventio stelae, linguis duabus scripturisque tribus inscriptae, eruditis Instituti Aegypti statim nuntiata est; ibi enim iussu imperatoris Napoleonis eruditi omnium scientiarum (sub aegide Commissionis Scientiarum et Artium) properaverant cum expeditione Francica. Qua a Britannis mox debellata, tabula Rosettana Londinium missa hodie apud Museum Britannicum iacet. Textus Graecus cito lectus interpretationi textuum Aegyptiorum (in formis hieroglyphica et demotica expressorum) gradatim adiuvit. Denique textum plene interpretatus est Ioannes Franciscus Champollion. Ab opere eruditorum cumulativo coepit hodiernus scripturae hieroglyphicae linguaeque Aegyptiae a...
Read more

How to label and detect the document text images

Image
1 $begingroup$ This is what I mean as document text image: I want to label the texts in image as separate blocks and my model should detect these labels as classes. NOTE: This is how the end result should be like: The labels like Block 1, Block 2, Block 3,.. should be Logo, Title, Date,.. Others, etc. Work done: First approach : I tried to implement this method via Object Detection, it didn't work. It didn't even detect any text. Second approach : Then I tried it using PixelLink. As this model is build for scene text detection, it detected each and every text in the image. But this method can detect multiple lines of text if the threshold values are increased. But I have no idea how do I add labels to the text blocks. PIXEL_CLS_WEIGHT_all_ones = 'PIXEL_CLS_WEIGHT_all_ones' PIXEL_C...
Read more

LSTM sequence prediction: 3d input to 2d output

Image
1 $begingroup$ I have this LSTM model model = Sequential() model.add(Masking(mask_value=0, input_shape=(timesteps, features))) model.add(LSTM(100, dropout=0.2, recurrent_dropout=0.2, return_sequences=False)) model.add(Dense(features, activation='softmax')) model.compile(loss='categorical_crossentropy', optimizer='adam', metrics=['accuracy']) and shapes X_train (21, 11, 5), y_train (21, 5) . Each timestep is represented by 5 features and return_sequences is set to False because I want to predict one 5D array (the next timestep) for each input sequence of 11 timesteps. I get the error ValueError: y_true and y_pred have different number of output (5!=1) If I reshape the data as X_train (21, 11, 5), y_train (21, 1, 5) instead I get the error ValueError: Inva...
Read more