# 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

## 1 Answer

The symbol "$\forall$" means "for all" or "for every".

"$\forall i \in \lbrace 0,1,2 \rbrace$" means "for all $i$ in the set $\lbrace 0,1,2 \rbrace$".

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thank you. It means i can only be 0,1,2 am I right, and nothing more basically? –  dan Jan 19 '12 at 15:26
@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
Why can't I get "\{" and "\}" to render (I've used them before here)? "\lbrace" and "\rbrace" work fine... –  David Mitra Jan 19 '12 at 15:30
ok I get it now, thanks to all of you guys! –  dan Jan 19 '12 at 15:32