$MachineEpsilon

$MachineEpsilon

gives the difference between 1.0 and the next-nearest number representable as a machine-precision number.

Details

  • $MachineEpsilon is typically 2-n+1, where n is the number of binary bits used in the internal representation of machine‐precision floating‐point numbers.
  • $MachineEpsilon measures the granularity of machine‐precision numbers.

Examples

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Basic Examples  (1)

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The result of adding 1 to $MachineEpsilon is distinct from 1:

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Adding a fraction of $MachineEpsilon effectively results in rounding:

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Scope  (2)

Applications  (2)

Properties & Relations  (3)

Neat Examples  (1)

Introduced in 1991
(2.0)