Category:Successor of Ordinal Smaller than Limit Ordinal is also Smaller

This category contains pages concerning Successor of Ordinal Smaller than Limit Ordinal is also Smaller:

Let $\On$ denote the class of all ordinals.

Let $\lambda \in \On$ be a limit ordinal.

Then:

$\forall \alpha \in \On: \alpha < \lambda \implies \alpha^+ < \lambda$