Simple condition in a Math expression

Question

Is there any simple math expression that returns $-1$ if $x > a$ or $1$ if $x < a$?

It can either be undefined at x = a, or -1 or 1. Doesn't matter to me. — Alon Gubkin, Oct 24 '13 at 13:20

Cameron Buie · Accepted Answer · 2013-10-24T19:25:41.163

4

To convert Daniel Fischer's perfectly good comment-answer into an actual answer: $$\frac{a-x}{|a-x|}$$

edited Oct 24 '13 at 19:25

answered Oct 24 '13 at 14:12

Cameron Buie

Hey, that's not true. I do that a lot. I just can't keep up with them all. – Daniel Fischer Oct 24 '13 at 18:13
Fair enough. It always strikes me that you (and David Mitra) leave a whole bunch of comment-answers, but I haven't seen many of your actual answers. – Cameron Buie Oct 24 '13 at 19:23
Odd. Our primary tags have a fair amount of overlap. – Daniel Fischer Oct 24 '13 at 19:30

score 3 · Answer 2 · answered Oct 24 '13 at 13:27

3

The simplest I know is $$f(x)= \begin {cases} 1 &x \lt a\\-1&x\gt a \end {cases}$$ This is a fine expression

answered Oct 24 '13 at 13:27

Ross Millikan

2 Answers2