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Discrete geometry is a branch of mathematics that studies geometric objects and properties in a discrete setting, as opposed to continuous geometry. It focuses on structures that are made up of distinct, separate elements rather than continuous shapes or surfaces. This can include the study of points, lines, polygons, polyhedra, and more complex shapes, particularly in finite or countable settings.

In discrete mathematics, a theorem refers to a statement that has been proven to be true based on previously established statements such as axioms, definitions, and other theorems. Theorems are integral to the field as they form the backbone of mathematical reasoning and structure. ### Key Components of Theorems in Discrete Mathematics: 1. **Definitions**: Before proving a theorem, precise definitions of terms involved are necessary to ensure clarity and avoid ambiguity.