machine eps related query

1 + eps > 1

ans =

logical

1

% as expcted

1 + eps

ans =

1.000000000000000

% unexpected, and indeed

1+2.5*eps

ans =

1.000000000000000

any help appreciated

Answer 1

[Ameer Hamza]

It happens because of finite precision of double() precision datatype: https://en.wikipedia.org/wiki/Double-precision_floating-point_format. Also, because of the fact that MATLAB only prints 16 digits by default, the remaining digits after conversion are not shown (double datatype cannot store more than 16 digits accurately). Try the following

>> fprintf('%0.20f\n', 1+eps)
1.00000000000000022204
>> fprintf('%0.20f\n', 1+2.5*eps)
1.00000000000000044409