Limit
A limit is the value a quantity approaches as its input is brought arbitrarily close to some point, whether or not the quantity ever reaches that value. The vague phrase "gets closer and closer" was made exact in the nineteenth century by the epsilon-delta definition: the output can be forced within any tolerance you name, provided the input is kept within a tolerance that can be found in response. Everything in calculus is defined by limits.
Why it matters
It is the idea that let mathematicians talk about the infinitely small without appealing to infinitely small quantities, which had been the weak point of calculus for two hundred years.
Also written: limits
Where it comes up
Sources
- Limit (mathematics) Wikipedia
- Calculus history MacTutor History of MathematicsTracks how the limit concept was forced on mathematicians by problems with the older approach.
