$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
open allclose allBasic Examples (1)
The result of adding 1 to $MachineEpsilon is distinct from 1:
Adding a fraction of $MachineEpsilon effectively results in rounding:
Scope (2)
Applications (2)
Properties & Relations (3)
Neat Examples (1)
See Also
Tutorials
Related Guides
Introduced in 1991
(2.0)