File:HomogeneousDiscontinuousFunction.gif
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HomogeneousDiscontinuousFunction.gif (360 × 289 pixels, file size: 7 KB, MIME type: image/gif)
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DescriptionHomogeneousDiscontinuousFunction.gif |
English: An example that shows that a homogeneous function does not have to be continuous. This is the function f defined by f(x,y)=x if xy>0 or f(x,y)=0 otherwise. It is homogeneous of order 1, i.e. f(a*x,a*y)=a*f(x,y). It is discontinuous at y=0, x=/=0. |
Date | |
Source |
Own work This diagram was created with Mathematica. |
Author | Sbyrnes321 |
(* Source code in Mathematica 6.0 by Steve Byrnes, 2011. *) eps = .001; a = Show[Plot3D[x, {x, 0, 1}, {y, eps, 1}, PlotRange -> {{-1, 1}, {-1, 1}, {-1, 1}}], Plot3D[0, {x, -1, 0}, {y, eps, 1}], Plot3D[0, {x, 0, 1}, {y, -1, -eps}], Plot3D[x, {x, -1, 0}, {y, -1, -eps}], Plot3D[x (1 - y/eps)/2, {x, -1, 0}, {y, -eps, eps}], Plot3D[x (1 - y/eps)/2, {x, 0, 1}, {y, -eps, eps}]] Export["pic.gif", a]
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This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication. | |
The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.
http://creativecommons.org/publicdomain/zero/1.0/deed.enCC0Creative Commons Zero, Public Domain Dedicationfalsefalse |
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 18:00, 16 February 2011 | 360 × 289 (7 KB) | Sbyrnes321 (talk | contribs) | {{Information |Description ={{en|1=An example that shows that a homogeneous function does not have to be continuous. This is the function f defined by f(x,y)=x if xy>0 or f(x,y)=0 otherwise. It is homogeneous of order 1, i.e. f(a*x,a*y)=a*f(x,y). It is |
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