The reason why the epsilon delta definition is so venerated is that it fits directly into well known methods of the formalization of mathematics, making the notion completely precise.
Basically, continuity, or higher order conditions like differentiability seem to impose greater constraints on problems, which make them more solvable.
Some good examples of that:
- complex discrete problems:
- simple continuous problems:
- characterization of Lie groups
Something that is very not continuous.
Notably studied in discrete mathematics.
Chuck Norris counted to infinity. Twice.
Articles by others on the same topic
In mathematics, a limit is a fundamental concept that describes the value that a function approaches as the input approaches a certain point. Limits are essential in calculus and analysis, serving as the foundation for defining derivatives and integrals. ### Formal Definition The formal definition of a limit uses the idea of approaching a certain point.