A funciton that finds the maximum between two values?

Question

Is there an $f$ that takes two values $a$ and $b$ and if $b>a$, it returns $f(a,b) = b-a$ otherwise $f(a,b) = 0$?

Is the $f$ linear?

P.S: I think one can find the maximum between $a$ and $b$ and then subtract $a$ from the maximum to get the desired $f$ described above.

By linear, you mean $F(x,y)=mx+ny$ for some constants $m,n$? Pretty clear that no $m,n$ work. Or did you mean something else? — lulu, Oct 17 '16 at 16:51
Linear function...on what set? Does that thing look "linear"? — DonAntonio, Oct 17 '16 at 16:51
The question could be more simply phrased by asking whether that function is linear. $\qquad$ — Michael Hardy, Oct 17 '16 at 16:52
@lulu A function that could be implemented linearly, like in a linear optimization problem. — Mahdi, Oct 17 '16 at 17:02
@Mehdi: The title and the body of your question do not match. Your $f$ does not return what you say: for instance, $f(1,0) = 0$ - it clearly does not return the maximum. — Alex M., Oct 17 '16 at 17:42
@AlexM. Thanks. the link you sent is very similar to my question and solves my problem. — Mahdi, Oct 17 '16 at 17:55

score 0 · Answer 1 · answered Oct 17 '16 at 16:52

0

The following is "almost" linear $$ \max\{a,b\}=\frac{a+b+|a-b|}{2} $$

answered Oct 17 '16 at 16:52

boaz

based on your comment I think $f$ could be $f(a,b) = \frac{a+b+|a-b|}{2} -a$. But why "almost" linear? – Mahdi Oct 17 '16 at 17:10
Why you need the $-a$? in the title you asked for the maximum. A linear function is one of the form $f(x_1,\ldots,x_n)=a_1 x_1+\ldots+a_nx_n$, not including absolute values. – boaz Oct 17 '16 at 17:14
You are right. What I really need is in the body of the question but actually did not know how to call an $f$ with such property. So I thought I can get the max and then use $-a$! How should such an $f$ be called? – Mahdi Oct 17 '16 at 17:17

1 Answers1