Discrete mathematics is the study of
mathematical structures that are fundamentally
discrete rather than . In contrast to
real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics – such as
integers,
graphs, and
statements in
logic – do not vary smoothly in this way, but have distinct, separated values. Discrete mathematics therefore excludes topics in "continuous mathematics" such as
calculus and
analysis. Discrete objects can often be
enumerated by integers. More formally, discrete mathematics has been characterized as the branch of mathematics dealing with
countable sets (sets that have the same cardinality as subsets of the natural numbers, including rational numbers but not real numbers). However, there is no exact definition of the term "discrete mathematics." Indeed, discrete mathematics is described less by what is included than by what is excluded: continuously varying quantities and related notions.