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Edited the question. One commenter said these functions are antisymmetric. Does that mean they're not symmetric? Symmetric to what exactly? What are some general characteristics.

Asker123
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    This certainly doesn't hold for all functions $f$. – Sean Roberson Dec 07 '17 at 21:12
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    Perhaps it holds for the function the teacher was talking about. – GEdgar Dec 07 '17 at 21:14
  • It sounds like this question is completely out of context. You need to think about what the teacher was showing you just before saying that $f(x,y)=-f(y,x).$ They must have said something about $f$ that would allow making this conclusion. If you can find anything in your notes, edit it into the question, even if the conclusion still doesn't make sense; it might help someone explain the reasoning. – David K Dec 07 '17 at 22:01
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    I suspect your teacher was talking about a specific function. There are some functions for which this is true but in general it is not true as you have probably discovered yourself. Example. It is not true for $f(x,y) = 3x +2xy + 7y\ne -3y-2xy -7x =-f(x,y)$ but it is true for $f(x,y) = x^2y - xy^2= -y^2x + yx^2 = -f(y,x)$ – fleablood Dec 07 '17 at 22:12
  • This particular kind of functions are called antisymmetric, but not all function of two variables is such. – zwim Dec 07 '17 at 22:34
  • Please, if you are ok, you can accept the answer and set it as solved. Thanks! – user Jan 24 '18 at 21:48

1 Answers1

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This is only true for some functions.

EG

$$f(x,y)=x^2-y^2=-f(y,x)=-(y^2-x^2)=x^2-y^2 $$

user
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