File:Uniform continuity animation.gif
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Uniform_continuity_animation.gif (288 × 177 pixels, file size: 12 KB, MIME type: image/gif, looped, 16 frames, 2.4 s)
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Summary
| Description |
English: animation showing a discontinuous function as a pointwise limit of continuous functions
mathematica source code: f[n_, x_] := Which[x <= 0, 0, 0 < x < 1/n, n x, 1/n ≤ x, 1]; Table[Plot[f[n^2, x - 1] + 1, {x, -1, 3}, PlotRange -> {{-1, 3}, {0, 2.2}}, PlotStyle -> {Thickness[ 0.02]}, Ticks -> False], {n, 1, 10}] Show[{Plot[f[100, x - 1] + 1, { x, -1, 0.9}, PlotRange -> {{-1, 3}, {0, 2.2}}, PlotStyle -> {Thickness[0.02]}, \ Ticks -> False], Plot[f[100, x - 1] + 1, {x, 1.1, 3}, PlotRange -> {{-1, 3}, {0, 2.2}}, PlotStyle -> {Thickness[0.02]}, Ticks -> False], Graphics[Circle[{1, 2}, 0.3]]} ]; Show[{Plot[f[100, x - 1] + 1, {x, -1, 0.9}, PlotRange -> {{-1, 3}, {0, 2.2}}, PlotStyle -> {Thickness[0.02]}, Ticks -> False], Plot[f[100, x - 1] + 1, {x, 1.1, 3}, PlotRange -> {{-1, 3}, {0, 2.2}}, PlotStyle -> {Thickness[0.02]}, Ticks -> False], Graphics[{ Disk[{1, 1}, 0.07], Circle[{1, 2}, 0.07]} ]} ]; |
| Date | |
| Source | Own work |
| Author | Jakob.scholbach |
Licensing
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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. |
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 21:32, 25 August 2011 | | 288 × 177 (12 KB) | Jakob.scholbach | better animation |
| 21:29, 25 August 2011 |  | 288 × 177 (8 KB) | Jakob.scholbach | {{Information |Description ={{en|1=animation showing a discontinuous function as a pointwise limit of continuous functions mathematica source code: <nowiki> f[n_, x_] := Which[x <= 0, 0, 0 < x < 1/n, n x, 1/n ≤ x, 1]; Table[Plot[f[n^2, x - |
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