Talk:Positive and negative parts

The 'negative part', as defined, is neither negative nor a part. So the definition is confusing. If a=b+c, then b and c may be called parts of a. So the negative part of a should be (a-|a|)/2 rather than -(a-|a|)/2. The positive part of a is still (a+|a|)/2. Bo Jacoby 11:19, 8 December 2005 (UTC)

Bo, you are too negative in here. Why not focus on the positive part instead? Oleg Alexandrov (talk) 19:50, 8 December 2005 (UTC)

That's the standard definition. See, for example, "Measure Theory", by Donald L. Cohn, ISBN 3-7643-3003-1, page 53:

The positive part f⁺ and the negative part f⁻ of f are the extended real-valued functions defined by

$f^{+}(x)=\max(f(x),0)$

and

$f^{-}(x)=-\min(f(x),0).$

Besides, there is a reason that the two functions be nonnegative: to be able to define Lebesgue integration, first on nonnegative functions and then on all functions. --Fibonacci 00:03, 9 December 2005 (UTC)

Relevance?

> A peculiarity of terminology is that the 'negative part' is neither negative nor a part (like the imaginary part of a complex number is neither imaginary nor a part).

Is this really relevant? It's not clear what the author means by "a part." No reference is provided for that term, and I don't know of any standard definition of it. The parenthetical is certainly not relevant, and I think that part at least should be removed.

Emgram (talk) 13:38, 8 July 2024 (UTC)