Mapping or projection is also used to define functions in mathematics and related fields. The mapping from non-empty set to non-empty set can only be one-to-one or many-to-one mapping. Maps have many names in different fields, which are essentially the same. Such as functions, operators, etc.
A function is a mapping between two sets of numbers, while other mappings are not functions. One-to-one mapping (bijection) is a special mapping, that is, the only correspondence between two groups of elements.
Extended data
Mapping calculation can realize cross-dimensional correspondence. The corresponding calculus belongs to pure digital calculation, so it is impossible to realize multidimensional correspondence. Differential simulation can realize complex simulation in this field. Mapping can approximate unrelated sets, while calculus can only accurately calculate a large number of continuous related sets.
The classification of mapping is based on the results of mapping, and the main classification includes: classification according to the geometric properties of the results, classification according to the analytical properties of the results, and consideration of geometric and analytical properties. Geometric features are divided into full projection and non-full projection; The analysis features are divided into single projection (one-to-one) and non-single projection; Geometric features and analytical features are also divided into full single projection.
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