Topology: Why do we consider the set $(2.9,3.1)$ open whereas $[2.9,3.1)$ is not considered to be open? 

My understanding of open sets is that an open set is one such that for an element $x$ in a set, we can find sort of a 'neighborhood' or distance more than $0$ (doesn't matter how small, so as long as it's more than $0$) that will still be in the set.

I understand that for $[2.9,3.1)$ if the point I select is on $2.9$ then any distance ($d$) from it would fall out of the set. But won't the same apply for the $(2.9,3.1)$ case as well? After all, $(2.9,3.1)$ spans a smaller range than $[2.9,3.1)$, so it stands to reason that if a point $2.9$ falls out of $[2.9,3.1)$, it will fall out of $(2.9, 3.1)$ as well.