Kappa ($\kappa$): The Largest Real Number, Constructed Through Limit Theory

We construct a real number $\kappa$, defined as the limit of the predecessor function $f(n) = n - 1$ as $n \to \infty$. The central argument is straightforward: \textbf{in mathematics, the limit of a function or sequence, when it exists as a value, is a real number.} Since $\kappa$ is defined as such a limit, it IS a real number. Furthermore, since at every finite step $n - 1 < n$, this strict inequality carries through the limit, giving us $\kappa < \infty$. Because $\kappa \neq \infty$ and $\kappa$ is a real number, it is finite. Yet it exceeds every explicitly nameable natural number. We conclude that $\kappa$ is the \textbf{largest real number before infinity.