Homogeneous nonlinear function

In summary, the conversation discusses finding a function that satisfies scalar multiplication but not addition. The participants suggest various examples, such as F(x,y) = |x| and f(x,y) = sqrt(x^2+y^2). However, it is pointed out that these examples do not satisfy the property for all values of a. The final suggestion is f(x,y) = (x^3+y^3)^(1/3), which is accepted as a better example. The conversation also touches on the definition of a function and the importance of mapping from R^2 to R.
  • #36
matt grime said:
So if i declare f(x)=x^2+y^2, and then declare g(x) to be the square root of f(x), in what way it that not sqrt(x^2+y^2)?

Very intereting posts and emotions. To be consistent with the original notations of matt, he could have written g(x) to be square root of f(x,y) and not f(x), as he defined f(x,y) and not f(x) to be x^2+y^2.
 
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  • #37
quantster said:
Very intereting posts and emotions. To be consistent with the original notations of matt, he could have written g(x) to be square root of f(x,y) and not f(x), as he defined f(x,y) and not f(x) to be x^2+y^2.

I was not planning to write but quantster raised a good point. In fact that was the beginning of the confusion.

In the future make sure to use consistent notations instead of assuming that people shall get some vibe from you and be able to read your mind.
 

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