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Braces enclosing a variable, a separator and a condition, defining a set by a rule.
Also known as: Set comprehension, Such that notation, Set abstraction
Set-builder notation defines a set by a rule rather than by listing its members: braces enclose a variable, a separator, and the condition the variable must satisfy. The separator is a vertical bar or a colon, and both are read aloud as 'such that'. Nothing on the page indicates that, which is why the notation is opaque until somebody says it out loud — and once they have, the whole construction reads as an English sentence.
Defines a set by the property its members share rather than by listing them, which is the only way to write down a set that is infinite or merely very large.
Contexts: Mathematics
Uses a vertical bar or a colon as its separator, and both are read aloud as 'such that'. Nothing in the printed form says so, which is why the notation is opaque until it has been read out once.
Contexts: Mathematics
A pair of curly braces enclosing a letter, then a single vertical line or a colon, then a short condition written after it.
Both belong to the notation of sets.