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Jul
8
accepted Conditions for functions to be independent of one of their variables
Jul
8
comment Conditions for functions to be independent of one of their variables
Oops. Well, it's now clear to me that I was mistaken about being able to extend the function, and that continuity is necessary for $x<0 \text{ and } y=0$ so that the derivative can exist for all of $A$. Thanks for your help. If you care to sum up the discussion in an answer, I'll accept it.
Jul
7
comment Conditions for functions to be independent of one of their variables
Best I can figure, is that it has to do with implicit continuity. That is, if we define a jump function, with a constant for $y\lt 0$ and another constant for $y\ge 0$, then the partial derivative is $0$, but $f(x,-1)\ne f(x,1)$. Is that about right?
Jul
7
asked Conditions for functions to be independent of one of their variables
Apr
13
awarded  Supporter
Jun
18
awarded  Scholar
Jun
18
accepted Upper bound on number of starting positions of a grid coloring game
Jun
18
comment Upper bound on number of starting positions of a grid coloring game
Noticing that the perimeter of the true squares remained invariant was clever. Thank you for your insight!
Jun
18
asked Upper bound on number of starting positions of a grid coloring game
Feb
25
awarded  Autobiographer