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mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...
, Kleene equality, or strong equality, (\simeq) is an equality operator on partial functions, that states that on a given argument either both functions are undefined, or both are defined and their values on that arguments are equal. For example, if we have partial functions f and g, f \simeq g means that for every x: * f(x) and g(x) are both defined and f(x) = g(x) * or f(x) and g(x) are both undefined. Some authors are using "quasi-equality", which is defined like this: (y_1 \sim y_2):\Leftrightarrow((y_1\downarrow \lor y_2\downarrow)\longrightarrow y_1=y_2), where the down arrow means that the term on the left side of it is defined. Then it becomes possible to define the strong equality in the following way: (f \simeq g):\Leftrightarrow (\forall x. (f(x)\sim g(x))).


References

* Computability theory Equivalence (mathematics) {{mathematics-stub