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What does this vertical line mean in an equation?

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That's not an equation. There's no equal sign.

The vertical line in a set, which this is (as indicated by the curly brackets), is read as "such that". In this form of defining a set, the part before the bar defines the kind of thing that is in the set, and the part after the bar is the rule that things in the set obey.

(Typo fixed. I said "part after the equals sign". I meant "part after the bar").

{x | -14 < x} says that members of this set are "x", so single numbers. Presumably real numbers. Usually it would say so explicitly, like {x ε R | -14 < x} which says things in the set are of the form REAL NUMBERS x that follow the rule -14 < x. As opposed to {x ε Z | -14 < x} which says things in the set are integers that follow that rule.

Then the rest says "such that -14 < x".

Which is equivalent to x > -14. So it's the set of (real?) numbers which are greater than -14.

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