Inequalities



-----maxima-admin@math.utexas.edu wrote: -----

>Ah, OK. Is there a reason they aren't boolean-valued?

Depending on context, a comparison might be boolean-valued
or it might be set-valued. So yes, there is a (good) reason
why comparisons aren't always boolean-valued.

Here is an example where the intended meaning of '<' is set-valued:

   (x + 2 < 1 + x) == (2 < 1) == empty set.

And an example where the intended meaning of '<' is boolean-valued:

   if (2 < 1) then a else b == if false then a else b == b.

The Maxima command 'solve' tries to evaluate the '=' comparison to a set:

   solve(x + 2 = 2, x) == [x = 0] == {0}.


Barton