If I have an interval $[a,b]$, where $a>b$, would it be defined? Would it be zero?
EDIT, to give an example why I asked: if I have $[a + 1/n, b - 1/n]$, where $n=1, 2, ..., inf$, do I have to impose any restriction on $n$? For example, when $a = 0$, $b = 1$ and $n=1$, I would have [a+1, b-1], i.e., [1, 0].
It depends on the context.
In most situations, if $a>b$, $[a,b]=\emptyset$.
In Riemann integration, if $a>b$, you might represent $\int_{[a,b]}f(x)dx=\int_a^bf(x)dx=-\int_b^af(x)dx$
In Lebesgue integration, if $a>b$, you might represent $\int_{[a,b]}f(x)dx=\int_{[b,a]}f(x)dx$.
After OP's edit: In the situation described by the OP, it is safe to treat $\left[a+\frac{1}{n},b-\frac{1}{n}\right]$ as empty whenever $n$ is too small because, for $n$ sufficiently large, the interval makes sense. Also, the OP wants to ignore the cases where $n$ is too small, anyway.