$\begingroup$I am taking a introductory course in numerical mathematics, using MATLAB and a numerical math text that refers to MATLAB often. In the text, the machine precision is defined as:
The distance $\epsilon$ between 1 and the next largest floating point number that can be represented in the system.
In MATLAB, the command help('eps') agrees, stating:
eps, with no arguments, is the distance from 1.0 to the next larger double precision number.
Now, my understanding is that this should mean that $1+\epsilon$ is the smallest number greater than 1 that can be represented, so we should have: $$1+0.9\epsilon = 1$$ $$1+\epsilon \ne 1$$
However, in MATLAB, the number that I intuitively understand to have the properties of $\epsilon$ seems to actually be just above $\epsilon/2$. Observe that the code
1+eps==1 1+eps*0.9==1 1+eps*0.51==1 1+eps*0.5==1 Produces the output:
ans = 0 ans = 0 ans = 0 ans = 1 How am I misinterpreting the definition of eps? Is is because some of these numbers are not normalized?
$\endgroup$8 Reset to default
