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$\begingroup$

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, 2.2012-01-19
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    totally agree, my bad.2012-01-19

1 Answers 1

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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?2012-01-19
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    @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 $2$.2012-01-19
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    Why can't I get "\{" and "\}" to render (I've used them before here)? "\lbrace" and "\rbrace" work fine...2012-01-19
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    ok I get it now, thanks to all of you guys!2012-01-19
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    And is there a prounounciation for it or if I see ∀α.r should I read that as "for all alpha dot r"?2016-02-07