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*From*: fl <freder...@xxxxxxxxxxx>*Date*: Sun, 24 Aug 2014 02:41:27 -0700 (PDT)*References*: <4bfacee9-8875-40d3-99f0-08f55455b42c@googlegroups.com>

Ordinary mathematics has no formal notion of a "partial function".

I have no exact definition of what the syntagm "ordinary mathematics" means but Bourbaki in his treatise

gave a definition of a function as a triple (F,A,B) where F is a part of ( A X B ) with extra conditons,

A the domain of the function and B the range. The reason for representing a function as a triple -- and not as

a part of cross product more simply -- is to include the case of partial function.

Here is an excerpt of wikipedia where Bourbaki's formalization of a function is given in full.

``In 1954, Bourbaki, on p. 76 in Chapitre II of Theorie des Ensembles (theory of sets), gave a definition of a function as a triple*f* = (*F*, *A*, *B*).^{[99]} Here *F* is a *functional graph*, meaning a set of pairs where no two pairs have the same first member. On p. 77 (*op. cit.*) Bourbaki states (literal translation): "Often we shall use, in the remainder of this Treatise, the word *function*instead of *functional graph*."''

http://en.wikipedia.org/wiki/History_of_the_function_concept#Bourbaki_1939

--

FL

**References**:**"Partial" Functions***From:*Leslie Lamport

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