Atlas of Fundamental Concepts

Follow von Neumann successor from the empty set to finite ordinals and $\omega$; pass by quotients, completions, and canonical embeddings through $\mathbb N$, $\mathbb Z$, $\mathbb Q$, $\mathbb R$, and $\mathbb C$; then continue through transfinite ordinals, alephs, beths, the continuum, and large cardinals. ZF is the baseline theory, Choice is shown explicitly, and statements independent of ZFC are labeled as such. This route separates abstract number systems from their chosen set-theoretic realizations.