Definition talk:Negative Part

Is this defined correctly?
I've just noticed how this is defined. It reflects the function in the $x$ axis, so when $f$ goes negative $f^-$ goes positive.

Is this right? I've been understanding it as a simple filter: a half-wave rectifier which does not invert, so it is the exact complement of the positive part.

Otherwise it would be called the "absolute value of the negative part" function.

If it is genuinely the way this function is actually defined, please explain this in a "historical note" sort of thing, explaining who it was originated that convention. --prime mover (talk) 22:38, 17 June 2022 (UTC)


 * I don't know the origin but can partially explain it. This decomposition was introduced to define the integral.
 * One defines the integral for all $f\ge 0$.
 * Then, one defines the integral for more general $f$ as:
 * $\int f := \int f^+ - \int f^-$
 * where $f = f^+ - f^-$
 * I guess the idea goes back to Henri Lebesgue.--Usagiop (talk) 23:40, 17 June 2022 (UTC)


 * What appallingly ill-designed rubbish. So why don't they define it as $f = f^+ + f^-$? Then the negative part will be the negative part and not the absolute value of the negative part. All mathematicians are stupid. --prime mover (talk) 05:05, 18 June 2022 (UTC)


 * I have invoked the Expand template so we as a mathematical community own to this festering pile of liquid faecal matter.