How is $\displaystyle \Delta I$ defined for $\displaystyle I$ some interval on $\displaystyle \mathbb{R}$? Is it just $\displaystyle sup(I)-inf(I)$, that is, the Supremum of the interval minus the Infimum?
How is $\displaystyle \Delta I$ defined for $\displaystyle I$ some interval on $\displaystyle \mathbb{R}$? Is it just $\displaystyle sup(I)-inf(I)$, that is, the Supremum of the interval minus the Infimum?
Thanks in advance.
Yes. More specifically, any interval, I, on R can be written in one of the forms (a, b), [a, b), (a, b], or [a, b]. In all of those cases $\displaystyle \Delta I= b- a$.