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.
Articles by others on the same topic
A continuous function is a type of mathematical function that is intuitively understood to "have no breaks, jumps, or holes" in its graph. More formally, a function \( f \) defined on an interval is continuous at a point \( c \) if the following three conditions are satisfied: 1. **Definition of the function at the point**: The function \( f \) must be defined at \( c \) (i.e., \( f(c) \) exists).