Notation: conditional formula How do I interpret the following equation:
$f(x) = 0.1 \cdot (1_{x>0} - 1_{x<0})$
What happens if x > 0 (let's say f(4))? Is this another way to express conditional formulas?
 A: Yes, this is a notation sometimes used to express conditional formulas.
The notation I like best is the one used in Concrete Mathematics, by Knuth et. al.:
[expression] means $1$ if the expression is true, $0$ otherwise.   Your formulat would be written
$$
f(x) = 0.1([x>0]-[x<0])
$$
At any rate, $f(4) = +0.1$.
A: If $x>0$, then $1_{x>0}(x)=1$ and  $ 1_{x<0}(x)=0$. Therefore, $f(x)=0.1$.
(I assume the notation $1_{P(x)}$ means the function that is $1$ if $P(x)$ is true and $0$ otherwise.)
A: The functions $1_{x>0}(x)$ and $1_{x<0}(x)$ are called characteristic functions and are shorthand for
$$1_{x>0}(x) = \begin{cases}
1, &x>0\\
0, &x\le 0,
\end{cases}\qquad 1_{x<0}(x) = \begin{cases}
1, &x<0\\
0, &x\ge 0
\end{cases}.$$
In general, the characteristic function $1_{A}(x)$ means
$$1_{A}(x) = \begin{cases}
1, &x\in A\\
0, &x\not\in A.
\end{cases}$$
In your case, the function
$$f(x) = 0.1 \cdot (1_{x>0} - 1_{x<0})$$
can be simplified to 
$$f(x) = \begin{cases} 
0.1, & x>0\\
-0.1, & x<0.
\end{cases}$$
