I see _. as indefinite, unknown, etc and multiplying (or dividing, and
several others)are still indefinite, unknown etc. So trying to say that
0*_. must be zero won't hold water ( what is the logical value for 0*_ or
0*__?) I can easily claim that _.*x must be indefinite for all x so that
_.*0 must be indefinite.
It seems to me that 0=x % _ for all x, but you must add an exception, is
just as true for _., its still indefinite.
Trying to extend arithmetic to the Reals (i.e. including infinities) has to
be careful.
Ralph S
On Fri, 8 Feb 2008, Mark D. Niemiec wrote:
Roger Hui <[EMAIL PROTECTED]> wrote:
The answer should be _. for the same reason that x+_. should be _. .
That is, for all numeric atoms x, _. should be the answer for
x + _.
x >. _.
x <. _.
_. + x
_. >. x
_. <. x
The rationale behind indefinites is that they represent a value
which could theoretically take on any number of different values
in the domain, but we have no idea of determining just which one
is appropriate.
In some cases, however, arithmetic involving _. CAN produce
non-indefinite results, when the result is totally independent
of the value of the indefinite. For example:
0 = 0 * _. NB. because 0 = 0 * y for all y
0 = _. % _ NB. because 0 = x % _ for all x (except _ and __)
By the same rationale, we should also have:
_ = _ >. _. NB. because _ = _ >. y for all y
1 = _ >: _. NB. because 1 = _ >: y for all y
(and similar for corresponding symmetrical and antisymmetrical cases)
-- Mark D. Niemiec <[EMAIL PROTECTED]>
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