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Regarding my previous question about the function $f(x,y)$ somebody claimed that $f(ax,ay)=af(x,y)$ is only true for "homogeneous" $x$ and $y$. Does anyone know what "homogeneous" means in this context?

cpiegore
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    A function $f(x,y)$ of two variables is called homogeneous if $f(ax,ay)=a^nf(x,y)$. The notion extends to arbitrary numbers of variables. – André Nicolas Feb 11 '16 at 03:25
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    It does not make sense to call the variables homogeneous. But it makes sense to call a function homogeneous. – bartgol Mar 03 '16 at 22:37

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A function $f(x,y)$ of two variables is called homogeneous if $f(ax,ay)=a^nf(x,y)$

cpiegore
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    A function of two variables is "homogeneous of degree n" if f(ax, ay)= a^n f(x, y)". "somebody claimed that f(ax,ay)=af(x,y) is only true for "homogeneous" x and y". Are you sure they didn't say "for f homogenous"? That is the definition of f(x,y) being homogeneous (of degree 1).

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     – user247327 Mar 03 '16 at 22:38