The Cell Is Finite — Numbers Have a Limit
Tier 2 begins the concrete work the first tier earned: how the world's contents — numbers of all sizes, text, images — actually become cell-sized numbers, and at what price. The first price is hiding in a phrase you accepted long ago without ceremony: a cell holds one number of limited size. Today that limit shows its teeth.
Start with the question
A car's odometer has six digit-wheels. It reads 999999. You drive one more kilometer. What does it show?
000000. Not because the car is broken — because six wheels can show exactly one million different readings and not one more; the seventh digit has nowhere to live, so it silently falls off the edge. Now the derivation, one step: a memory cell holds a number of limited size (the memory assumption, standing since the first lesson) — so a cell is an odometer. Any agreement about numbers in cells therefore has a largest and a smallest representable value. Not "very big numbers are slow" — representable at all or not, a hard edge, drawn by the cell before any program runs.
The universal word for driving past the edge is overflow — learn it once; it will meet you in every language, every system, and (a promissory note the course will honor in its final tier) in a disturbing share of famous security failures.
Two fates at the edge — and why the quiet one is worse
What happens ON the edge is not decided by the cell — the cell just is; it is decided by agreement, like every meaning in this course. Two honest designs exist: