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Definition: A set of data is said to be continuous if the values belonging to the set can take on ANY value within a finite or infinite interval. Definition: A set of data is said to be discrete if the values belonging to the set are distinct and separate (unconnected values).
Discrete mathematics is that which is done using finite methods typically using just the integers (e.g. combinatorics, elementary number theory) or at most a finite subset of the rationals, (e.g. discrete probability theory).
A function f is continuous when, for every value c in its Domain: f(c) is defined, and. limx→c f(x) = f(c) "the limit of f(x) as x approaches c equals f(c)"
Continuous functions are defined for all real numbers and have a smooth, unbroken graph. They can take on any value within a given interval. In contrast, discrete functions are defined only for specific, distinct values and have a graph that consists of isolated points.
Discrete mathematics is the study of mathematical structures that can be considered "discrete" (in a way analogous to discrete variables, having a bijection with the set of natural numbers) rather than "continuous" (analogously to continuous functions).
1 mar 2007 · In continuous math, we do that using differential equations, which are functions that describe the rate of change of one function using another derived function. In discrete math, we do the same thing using recurrence relations, which define a the value of a function at a point in terms of one or more of the points that precede it.
Continuous functions have a smooth and connected graph, without any abrupt changes or jumps. On the other hand, discrete functions have a graph consisting of isolated points, with no lines connecting them. For example, consider a continuous function such as f (x) = sin (x).
