Is it a mistake that the function sum?

Please see the follow code:

N=3;
sum(sum(eye(N)-ones(N,N)/N))

The MATLAB answer is 3.3307e-16, but the right answer is 0.

But it is true if N is 2, 4, 8 as follows:

N=2;
sum(sum(eye(N)-ones(N,N)/N))
N=4;
sum(sum(eye(N)-ones(N,N)/N))
N=8;
sum(sum(eye(N)-ones(N,N)/N))

These right answers are 0, and the MATLAB answer is 0 too.

Answer 1

[James Tursa]

Welcome to the world of floating point arithmetic.

https://www.mathworks.com/matlabcentral/answers/57444-faq-why-is-0-3-0-2-0-1-not-equal-to-zero