Symbol meaning

What Does a Vertical Bar Mean in Math?

Distinguish absolute value, divisibility, set-builder conditions, conditional probability, determinants, and evaluation bars.

Compare the possible meanings

NotationTypical meaningHow to identify it
|x|Absolute value or magnitudeThe bars enclose one expression
a | bDivisibilityA relation between integers
P(A | B)Conditional probabilityInside probability notation
{x | x > 0}Such thatInside set-builder notation
det |A|Determinant in some textsApplied to a matrix

Examples

  • |−3|=3 because absolute value is distance from zero.
  • 3|12 means 3 divides 12.
  • P(A|B) reads probability of A given B.

How to decide

Read the complete expression, identify the mathematical subject, and check whether the bars enclose an object or separate two statements.

How to verify the interpretation

Replace the bar with the proposed meaning in words. If the sentence becomes grammatically and mathematically coherent, the interpretation is plausible.

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