Re: Multiple return values

marssaxman < (Mars Saxman) marssaxman@sprynet.com> wrote:
)> I think it is an artefact of the origin of the "function" concept. The
)> idea of a function in maths is that you give it some parameters and it
) ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
)> performs some calculation on them. The result of the calculation is
)> the return value. It doesn't make sense to have, for example, an
)> arctangent return more than one value. Given the origins of computing
)> in maths it is easy to see why this habit has been carried on.


Mark Tillotson <markt@harlequin.co.uk> wrote:
)Huh? Mathematically a function is simply a many-1 binary relation
)defined for the whole of its domain. Any talk of more than one
)argument is shorthand for using cartesian products, which you can do
)with the result just as easily. In fact functions really don't have
)anything to do with calculation!!


[snip]


This is not true. A function f:RxR -> R is different from a function
taking two real arguments. The first is a unary function, the second
is a binary function. They are -not- the same thing. Derivatives and
integrals, in particular, are not the same. Didn't you learn that a
multiple integral was equivalent to an iterated integral, but not the
same? Is it also not obvious that a partial derivative is different
from a total derivative?


Mike
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