We present a graded extension of the complex numbers, integrating both infinitary and infinitesimal scales in a unified, hierarchical framework, which we refer to as the \emph{Omega number system}. Our construction is anchored by a fundamental scaling element, \(\Omega\), defined as the hyperreal corresponding to the equivalence class of the standard sequence \((1,2,3,\dots)\) via the ultrapower construction. Central to our approach is the lifting function \(L^\Omega(n)\), which elevates \(\Omega\) into a graded hierarchy so that the index \(n=0\) corresponds to the classical (finite) complex domain, \(n>0\) to increasingly large (infinitary) magnitudes, and \(n<0\) to infinitesimal values. From \(\Omega\) and \(L^\Omega(n)\) we derive key foundational objects, including the \emph{absolute zero} \(\underline{0}\), the graded continuum of \emph{almost zero} \(\overline{0}\), and its distinguished member, the \emph{canonical zero}, \(0^*=\Omega^{-1}\); which together with the identity \(1\), extend classical arithmetic coherently. We illustrate our approach through two foundational models: a linear (polynomial) model that extends familiar arithmetic via a straightforward graded extension and a non-linear (exponential) model incorporating exponential transfinite index growth. Moreover, by analysing selected elementary functions, we present concrete examples that include multivalued and probabilistic interpretations. We also introduce an enhanced non-linear system featuring multiplicative product-lifting, in which the generator function is defined through the additive components of Riemann’s zeta function, \(\zeta(s)\). Using this connection, we obtain the result that the negative and positive real \(\Omega\) limits of \(\zeta(s)\) are precisely characterized by the complete sequence of infinitesimal and infinitary canonical base elements, respectively. We further define a \emph{rank-lifting} of model families by introducing a rank-ordering of the fundamental scaling elements, \(^{r}\Omega\), for each tetration rank of \(\Omega\). For each rank \(r\), we associate a corresponding family of models, thereby extending \(\mathbb{O}\) to \({}^{r}\mathbb{O}\). We then analyze the special graded functions in \(\mathbb{O}\), including the \emph{reflection} operator \(R\!\bigl(\sum a_nL^\Omega(n)\bigr):=\sum a_nL^\Omega(-n)\), with selected examples showing deep and unexpected symmetries between infinitesimals and infinitaries. Leveraging these symmetries, we establish the graded Omega–zeta reflection identity \(R\!\bigl(\zeta(s+\Omega)\bigr)=\zeta\!\bigl(1-s-\Omega\bigr)\), which exchanges the two saturated real-\(\Omega\) limits of \(\zeta(s)\) and motivates a set of \emph{transposition} methods that systematically translate results between the infinitesimal and infinitary regimes. Building on these dualities, we develop an $\Omega$–operator algebra, generated by grade–shifts, reflection, parity, and phase twists; which furnishes discrete ladder symmetries, a scale–phase uncertainty principle, and a $C^{\!*}$-algebraic framework for renormalisation‐group flow. Finally, we discuss potential applications, such as the reinterpretation of classical singularities and the regularization of divergent behaviours. With this introductory work we aim to demonstrate that the Omega number system offers a flexible foundation for further analytical developments, paving the way for a full exposition of \emph{Omega analysis}, an extension of classical complex analysis into the transarchimedean domain of hierarchically graded infinitesimals and infinitaries.