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seen Dec 26 '13 at 0:47

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Dec
9
comment Gap exponents and homogeneous functions
@Ignore my last comment, I think I understand. So $g_f(x)$ is not strictly speaking a homogeneous function, but in the large and small limits of $x$ behaves approximately like a homogeneous function...?
Dec
9
comment Gap exponents and homogeneous functions
If you have a homogeneous function $g_f(x)$ of order $k>0$ then its limit should be $0$. If it's of order $0$ then it is independent of $x$. (I think I am missing something.) So here is my confusion. If we assume that it's homogeneous of order $0$, then even in the limit that $x$ gets large it shouldn't change.
Dec
9
comment Gap exponents and homogeneous functions
this is circular reasoning, no? We show the limit is fixed by fixing the limit...
Dec
9
comment Gap exponents and homogeneous functions
Thanks. Adam, do you mind elaborating specifically on how you get that $\lim {x \to 0} g_f(x)=c$ Why doesn't $c=0$? Edit to comment: looking at your last line I think is what I needed. How do you show that $b=0$?
Dec
9
asked Gap exponents and homogeneous functions