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

Adding a fraction of $MachineEpsilon effectively results in rounding:

The result of subtracting $MachineEpsilon/2 from 1 is distinct from 1:

Find machine epsilon algorithmically:

Get the nearest machine number greater than another machine number:

and are distinct:

and differ only in the least significant bit:

Horner's method for evaluating a polynomial with a running error bound:

A polynomial with large coefficients:

Evaluate at x=10; the error is large, but within the bound:

$MachineEpsilon is a power of 2:

$MachineEpsilon is twice 10^{-MachinePrecision}:

This is effectively where is the number of bits of machine precision:

1 and 1+$MachineEpsilon differ only in the least significant bit:

The resolution of machine numbers is twice as fine just below 1 versus just above 1: