The limitsneaking up on a point
Two points squeezed to one gives 0/0 nonsense — unless you sneak up and read where the journey is heading.
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A slope takes two points — rise over run. Move the second point onto the first and both go to zero. Zero divided by zero isn't infinity, isn't zero — it isn't anything. The recipe that works everywhere else quits.
The fix isn't to land on the point. It's to refuse to. Bring the second point close and take a slope reading. Three. Two point five. Two point one. Two point oh one. Two point zero zero one. Every step closer is a legal division with a real answer.
Those readings close in on two — each step locks in another digit. The value a process homes in on, without ever arriving, is called the limit.
One-sided evidence proves nothing, so run the same approach from the other side. One point nine. One point nine nine. One point nine nine nine. Climbing this time instead of falling — aimed at the same value. Both directions agree: two.
The limit is a promise, not an arrival. The two points never touch, so zero over zero never happens — we just read off where the journey was headed. The recipe that quit at the point still hands over an exact answer, because it was never asked to land there.