Math function to filter negative numbers

Question

Is there any standard math function for this operation:

f(x)=max(x,0)

I was wondering maybe there is a well-known function for this operation in mathematics literature.

Any idea?

Answer 1

This is usually denoted as (x)₊, sometimes also x⊔0 or x∨0, where the symbol alludes to the shape of the kinks in the maximum of two functions, for instance in |x|=max(x,-x).

In Lebesgue integration theory, for example, a function is first split into its positive and negative part, so that the integration theory can be reduced to non-negative functions.

Another application is splines, the cubic B-spline has the representation

B₃(x)=1/6 * ( (x+2)₊³ - 4 * (x+1)₊³ + 6 * (x)₊³ - 4 * (x-1)₊³ + (x-2)₊³ )

Answer 2

I guess, you are looking for:

(abs(x)+x)/2

https://www.wolframalpha.com/input/?i=%28%7Cx%7C%2Bx%29%2F2

Answer 3

Another way it might be characterised is as

x H(x)

where H(x) is the Heaviside unit step function.

H(x) = ( x >= 0 ? 1 : 0 )

i.e. 1 for positive x, 0 for negative x and either 0, 1, or 1/2 at x=0. This is used in control theory, signal processing and Fourier analysis. Its quite common to use f(x) H(x) for functions which start at a particular time, say switching some electronics on. So in this area of study x H(x) might be the best way to answer your question.