functions

[Leonard Soicher]

A problem with option 1 is that we may not know (or want to compute)
the actual preimages, but still may want to list the function images or
the numbers of objects mapping to given images. Another problem with
option 1 is that it might be very difficult to check that incoming data
is ordered correctly.

I have a question.  Might we ever want to mix the various types
of map_entry for a given "function", e.g. give explicit preimages for
some images and just the preimage cardinalities for others? Or should
we forbid this sort of thing?

-Leonard

>
>I would rule out 2,3,4 but am a little wary of throwing away the information in 
>the natural order. What is gained by doing so? Isn't option 1 in fact 'least in 
>clash with the "real" function' case? If option 5 offers a gain, then go with 
>it, but if not, my recommendation is for option 1.
>

>>>
>>>    1 keep the original "natural" order induced by the preimages from
>>>      which <preimage_cardinality>-s or <blank>-s were produced by
>>>      "contraction".
>>>
>>>