Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. Real numbers and rational numbers have the property that between any two numbers a third can be found, and consequently these numbers vary "smoothly". The objects generally 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 mathematics has also been characterised as the branch of mathematics dealing with countable sets (including rational numbers but not real numbers), and there is unfortunately no exact, universally agreed, definition of the term. Indeed, it is less what is included than what is excluded (the notions of a continuously varying quantity and related notions) that describes discrete mathematics.

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