Unsupported titles/Enclosing vertical lines

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1. (mathematics) Marks absolute value.

   |-3| = 3

   The absolute value of minus three is three.

   For x = (1,1), and y = (4,5), |x – y| = √([1–4]² + [1–5]²) = 5

   For x equals one, one and y equals four, five, the absolute value of the quantity x minus y is the square root of (open parentheses) the quantity one minus four squared plus the quantity one minus five squared (close parentheses) or five.

2. (mathematics) Marks determinants.

   |A|

   The determinant of the matrix A

3. (mathematics) Marks the operation of finding the cardinality of a set.

   ${\displaystyle \left|\{3,5,7,9\}\right|=4}$

   The set three, five, seven, and nine has a cardinality of four.

4. (mathematics) Notes the number of connected components.

   ${\displaystyle \left|S^{0}\right|=2}$

5. See ‖ for the caesura used individually, and see ‖ ‖ for two caesuras enclosing other text.

• (cardinality): #, card