Departure question
Catch change and accumulationPort 2 of 18Follow the languages built to calculate a world that will not stand still, from planets and fluids to waves, optimization, and chaos.
This voyage is an editorial path for understanding, not a claim of direct historical influence or sole invention.
"Can making x sufficiently close to a force f(x) as close to L as desired?" Seventeenth-century limit intuitions were refined through nineteenth-century work by Bolzano, Cauchy, Weierstrass, and others into ε-δ language. Continuity at a point means that the limit there equals the function value. Limits are central to analysis, though not every theory of differentiation or integration is built from this one definition alone.
The rigorous formalization of "approaching" via ε-δ — the foundation of all of calculus.
Q.lim_{x→0} sin(x)/x
Q.f(x) = 1/x as x → 0
Ports in time
Follow the scenes to see problems, notation, standards of proof, and applications changing across different times and places.
The method of exhaustion trapped areas between increasingly accurate polygonal bounds, anticipating the logic of limits centuries before modern notation.
No reliable place is given, so time continues without an invented pin
Continue through the world of this yearNewton described calculus through flowing and vanishing quantities. The method was powerful, but critics such as Bishop Berkeley attacked its “ghosts of departed quantities.”
No reliable place is given, so time continues without an invented pin
Continue through the world of this yearCauchy formulated limits and continuity through inequalities and arbitrarily small differences, creating a direct precursor of epsilon–delta analysis.
The recorded place matches a canonical map anchor
Continue this scene on the mapWeierstrass removed appeals to motion and intuition from limits, establishing the precise epsilon–delta language of modern analysis.
The recorded place matches a canonical map anchor
Continue this scene on the mapCompleteness of the real numbers, convergence in numerical analysis, asymptotic statistics, and probability limit theorems — the concepts that removed ambiguity from calculus.
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No concept belongs to one person
These are not inventor credits. They are different ports: opening a problem, sharpening a language, or carrying it into another world.
Number lenses
These numbers are editorial lenses for the voyage, not required prerequisites.
Follow the languages built to calculate a world that will not stand still, from planets and fluids to waves, optimization, and chaos.
Open the number voyage
Follow the languages built to calculate a world that will not stand still, from planets and fluids to waves, optimization, and chaos.
Open the number voyage
Follow the languages built to calculate a world that will not stand still, from planets and fluids to waves, optimization, and chaos.
Open the number voyage
Concept genealogy
Concepts arriving from before
Current port
Limit and Continuity
Concepts opened from here
Only direct editorial links are shown; this is not a complete learning order or historical influence line.
