**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.