# Is there a shorthand notation for the operation of saturation

1. Jul 6, 2010

### stevenb

I'd like to know if there is an accepted shorthand mathematical notation for the operation of saturation. Saturation basically means to take the output of any functional operation (or operator) and subject the final answer to limits.

For example, I might have the function y=2x, and might want to limit the output to the range 0 to 10. To notate this, there are a few options; for example.

y=0 if x<0; y=2x if 0<x<5; y=10 if x>5

or, y=0 if 2x<0; y=2x if 0<2x<10; y=10 if 2x>10

or, u=2x; y=0 if u<0; y=10 if u>10; y=u otherwise

This case by case method is becoming awkward in some work I'm doing which involves using saturation functions often. Right now, I'm using my own shorthand notation as follows:

$$y={\rm sat}_0^{10} \{2x\}$$

This works fine for my purposes, but I'd like to use an accepted notation if one exists.

Any help is appreciated.

2. Jul 6, 2010

### mathman

Usual notation would have y=max(0,min(10,2x))

3. Jul 6, 2010

### stevenb

Ah, I like that, and it works for my purposes. Thank you very much!