Thematics Of Order

[Jon Awbrey]

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TOO.  Note 4

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Re: TOO.  http://stderr.org/pipermail/inquiry/2005-April/thread.html#2541

Some useful conventions, by way of preliminary:

  +M  =  {+1, +2, +3, ...}  =  M

  -M  =  {-1, -2, -3, ...}

  0M  =  {0}

   B  =  {0, +}

   T  =  {-, 0, +}

   N  =  0M |_| M  =  B x M

   Z  =  -M |_| N  =  T x M

Consider the difference between two positive integers
as a function from ordered pairs of positive integers
to a 3-valued sign character and a positive integer,
in other words, diff : M x M -> Z = T x M.  If the
sign character of the functional value is 0, then
it is a matter of indifference what the attached
positive integer happens to be, so it might as
well be left in a _|_ or undefined condition.

Jon Awbrey

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inquiry e-lab: http://stderr.org/pipermail/inquiry/
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