File:HomogeneousDiscontinuousFunction.gif
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Summary
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.
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 09:28, 14 January 2017 | | 360 × 289 (7 KB) | 127.0.0.1 (talk) | 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. |
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