# Reading equations: Upside down A

what does this equation mean? I´m really bad in reading those, so if somebody explained it, I would really appreciate.

$f_i(x,y)\ge 0\quad\forall i\{0,1,2\}$

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Personal pet peeve: It is not an equation. An equation is a statement that two things are equal (has an equals sign). Your question involves the statement that $f_i(x,y)\geq0$ if $i$ is 0,1, 2. –  MJoszef Jan 19 '12 at 16:12
totally agree, my bad. –  dan Jan 19 '12 at 16:30

The symbol "$\forall$" means "for all" or "for every".
"$\forall i \in \lbrace 0,1,2 \rbrace$" means "for all $i$ in the set $\lbrace 0,1,2 \rbrace$".
@dan: It means that the statement is true for each of these three values of $i$: $f_0(x,y)\ge 0$, $f_1(x,y)\ge 0$, and $f_2(x,y)\ge 0$. It says nothing about $f_i(x,y)$ if $i$ is not $0,1$, or $2$. –  Brian M. Scott Jan 19 '12 at 15:28