I'm reading something on ordinal numbers and I have a silly notational doubt on them.
From a notational point of view, if $\gamma$ is a non limit ordinal, does the notation $\gamma-1$ make sense in order to denote the precedessor of $\gamma$? I'm asking this because I would define a sequence of sets of the form $X_\alpha=\Gamma(X_{\alpha-1})$ when $\alpha$ is non limit and $X_\alpha=\bigcup\limits_{\beta <\alpha} \Gamma(X_\beta)$ (here $\Gamma$ is a given function!), and I'm not sure that such a definition is correct, unless I do not assume the possibility of denoting the predecessor of $\gamma$ as $\gamma-1$.