File:Relative numbers representation.svg

Original file(SVG file, nominally 512 × 494 pixels, file size: 11 KB)

Summary

Description
English: A figure representing the equivalence classes of the relative numbers constructed as a pair of natural numbers. Any relative number (eg. -5) has an infinity of equivalent possible representation, eg. (2,7), (0,5), … The equivalent representations (in red) are on the same blue dotted line, and the number in blue at the end on the line is the corresponding relative number
Français : Une figure représentant les classes d'équivalences entres les paire d'entiers construisant les nombre relatifs.

Chaque nombre relatif (par exemple -5) a une infinité de paire qui le représentent de manière équivalente, (par exemple (2,7), (0,5).

Toutes ces représentation équivalente sont sur la même pointillé bleu, et le nombre relatif qu'elle représentent est au bout de la ligne.
Date
Source Own work
Author TomdFr
Other versions File:Relatives Numbers Representation.png
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This diagram was created with Asymptote.

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Generation code

In asymptote programming language (w:Asymptote (vector graphics language))

// import settings; import graph;  // pdfviewer="evince"; // psviewer="evince";  // returns a pair representation of a relative number of the equivalent class pair pairRepresentation(int n){ 	if(n>0){ 		return(n,0); 	}else{ 		return(0,-n); 	} }  string nullString(real r){ 	return ""; }  void drawCoordinates(pair point, align align=NoAlign){ 	label("$("+string(point.x)+","+string(point.y)+")$",point,align); }  unitsize(50,50);  int num = 10; int i;  for (i=-1*num ; i<=num ; ++i) { 	pair point = pairRepresentation(i) ; 	dot(point,red);  	// equivalence classes labelled with usual names, in blue 	label("$\mathbf{"+string(i)+"}$",point,5SW,fontsize(17)+blue);  	int j; 	for(j=abs(i);j<num;++j) { 		drawCoordinates(point,E); 		pair nextpoint = point + (1,1);  		draw(point -- nextpoint,blue+Dotted+linewidth(2)); 		dot(point,red+linewidth(5));  		point=nextpoint; 	} 	dot(point,red); 	draw(point -- point+(0.5,0.5),blue+Dotted+linewidth(2)); 	dot(point,red+linewidth(5)); 	drawCoordinates(point,E); }  // axes  real decay=-0.2;  ticks tick=RightTicks(N=0,n=1,end=false,nullString); xaxis("$n_1$",YEquals(decay),decay,num+1.0,tick,Arrow); yaxis("$n_2$",XEquals(decay),decay,num+1.0,LeftTicks(N=0,n=1,end=false,nullString),Arrow); 

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25 November 2009

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Date/TimeThumbnailDimensionsUserComment
current03:00, 31 January 2018Thumbnail for version as of 03:00, 31 January 2018512 × 494 (11 KB)Perhelionfix librsvg bug phab:T35245
21:57, 25 November 2009Thumbnail for version as of 21:57, 25 November 2009429 × 414 (81 KB)TomdFrUploaded a version from -5 to 5, -10 to 10 was uselessly too big.
20:05, 25 November 2009Thumbnail for version as of 20:05, 25 November 2009754 × 727 (244 KB)TomdFr{{Information |Description={{en|1=A figure representing the equivalence classes of the relative numbers constructed as a pair of natural numbers. Any relative number (eg. -5) has an infinity of equivalent possible representation, eg. (2,7), (0,5), ... The
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