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Reversible function

Reversible function

A function is called a reversibly unique (one-to-one) function if not only a function value is uniquely assigned to each argument - , but also, conversely, exactly one argument belongs to each function value.

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If one buys buns of a certain type from a baker, the price to be paid is uniquely determined by the number of buns purchased - matlab homework help . If each student of a group rolls the dice exactly once with a normal playing dice, the number of dice rolled can be assigned uniquely to each student in this way: In both cases, then, we are dealing with unambiguous assignments - the rules describe functions.

Nevertheless, from a mathematical point of view, there is a significant difference between the two situations described: while in the first case, a certain number of buns clearly belongs to each price indication (precisely the number of buns that one receives for the money), the assignment "number of dice rolled → student" is not unique, since several students may have rolled the same number of dice (which is, after all, unavoidable with more than six players).

Generally speaking: In the first case, the assignment is unambiguous in both directions; in the second case, it is unambiguous only in the initial direction, but not in the reverse direction.

One says:

An assignment (mapping) is called reversibly unique (one-to-one), if by it not only to each element of the definition range an element of the value range is uniquely assigned - accounting homework helper , but also vice versa to an element of the value range exactly one element of the definition range belongs. In both directions the mapping represents a function - the function is reversible.

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