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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). Objects studied in discrete mathematics include integers, graphs, and statements in logic.
Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous.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 [1] – do not vary smoothly in this way, but have distinct, separated values. [2]
In signal processing and machine learning, discrete calculus allows for appropriate definitions of operators (e.g., convolution), level set optimization and other key functions for neural network analysis on graph structures. [3] Discrete calculus can be used in conjunction with other mathematical disciplines.
An illustration of Cantor's diagonal argument (in base 2) for the existence of uncountable sets.The sequence at the bottom cannot occur anywhere in the enumeration of sequences above.
Discrete Analysis; Discrete & Computational Geometry; Discrete Applied Mathematics; Discrete Mathematics; Discrete Mathematics & Theoretical Computer Science; Discrete Optimization; Discussiones Mathematicae Graph Theory; Electronic Journal of Combinatorics; European Journal of Combinatorics; The Fibonacci Quarterly; Finite Fields and Their ...
A discrete subgroup H of G is cocompact if there is a compact subset K of G such that HK = G. Discrete normal subgroups play an important role in the theory of covering groups and locally isomorphic groups. A discrete normal subgroup of a connected group G necessarily lies in the center of G and is therefore abelian. Other properties:
That is, the discrete space is free on the set in the category of topological spaces and continuous maps or in the category of uniform spaces and uniformly continuous maps. These facts are examples of a much broader phenomenon, in which discrete structures are usually free on sets.
Strongly discrete. Set D {\displaystyle D} is strongly discrete subset of the space X {\displaystyle X} if the points in D {\displaystyle D} may be separated by pairwise disjoint neighborhoods. Space X {\displaystyle X} is said to be strongly discrete if every non-isolated point of X {\displaystyle X} is the accumulation point of some strongly ...