The notion of function in F#
Let's begin with an intuitive definition of a function that many of us heard in school algebra class: function is a relationship that for each valid input yields a single consistent result. Such definition is a good enough to reflect both the commonality and the difference of functions and relations. In mathematics, a function is a relation, although not each relation is a function, as a relation may represent multiple results for the same single input. In the following figure, relation Rij on the left side is just fine for the representation of a function, as any item from set I maps to the one and only one item of set J. However, relation Rxy on the right side of the same figure cannot represent a function as at least one item of X exists, which maps to more than one item of Y, which is indicated by red mapping arrows.
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Relations and functions
Another very important matter is the mapping consistency. Any function, when being repeatedly given the same input must...