File:Limit point (vs subsequential limit).svg

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Original file ‎(SVG file, nominally 92 × 284 pixels, file size: 119 KB)

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Summary[edit]

Description
English:
Date
Source Own work
Author Physis
SVG development
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The SVG code is valid.
 
This vector image was created with Asymptote.
Source code
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Written in Asymptote, a vector graphics programming language code

dvisvgm 1.0.4 (i686-pc-linux-gnu) 
import graph;
usepackage("amsfonts");

size(10cm, 10cm, IgnoreAspect);

side further = Relative(N);

int till = 12;

xaxis(Label("$n \in \mathbb N$", 6further), 0, till + 0.9, Ticks(Step = 1, modify = NoZero), Arrow);
yaxis(Label("$a_n \in \mathbb R$", 3further), 0, 1.15, Ticks(Step = 1, modify = NoZero), Arrow, autorotate = false);
label("0", (0, 0), SW);

real a(int n) {return n % 2 == 1 ? 1 / n : 1;}

pen toggle (int n) {return n % 2 == 1 ? red : blue;}

for (int n = 0; n <= till; ++n)
	dot((n, a(n)), toggle(n) + 6);

shipout("Subsequential limit (vs limit point)");

erase();
size(0, 10cm);
// Either erase() or (re)size gets automatic scaling disabled, consequently, Ticks(N = ...) works no more

yaxis(Label("$\left\{\, a_n \in \mathbb R  \,\middle|\, n \in \mathbb N \,\right\}$", 3further), 0, 1.1, Ticks(Step = 1), Arrow, autorotate = false);

pen toggle2 (int n) {
	pen p = toggle(n);
	real w = linewidth(p);
	return n  == 1 ? p = p + (w + 6) : p;}

for (int n = 0; n <= 1000; ++n)
	dot((0, a(n)), toggle2(n));

shipout("Limit point (vs subsequential limit)");

Licensing[edit]

I, the copyright holder of this work, hereby publish it under the following licenses:
w:en:Creative Commons
attribution share alike
This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.
You are free:
  • to share – to copy, distribute and transmit the work
  • to remix – to adapt the work
Under the following conditions:
  • attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
  • share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
GNU head Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.
You may select the license of your choice.

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Date/TimeThumbnailDimensionsUserComment
current06:40, 25 March 2011Thumbnail for version as of 06:40, 25 March 201192 × 284 (119 KB)Physis (talk | contribs){{Information |Description ={{en|1=Image of the sequence}} |Source ={{own}} |Author =Physis |Date = |Permission = |other_versions = }} Category:Basics of topology

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