"Randy Poe" <rpoePA@yahoo.com> wrote in message
news:kplpmv017s5rkh4l0obo3cn30gvrutpo93@4ax.com...
> On Sat, 20 Sep 2003 11:34:20 +0100, "AndroclesInEngland"
> <jp006f9750@blueyonder.co.uk> wrote:
>
> > Hence (A xor B) does NOT imply [all of] (A or B),
>
> "imply all of"? What does that mean? (A xor B) means that either
> property A is true or property B is true, but not both. For example,
> let A = "X is a dog" and B = "X > 50 kg".  If X is an adult elephant,
> (A xor B) is true. If X is a 75 kg St. Bernard, (A xor B) is false.
> Clear?
>
> OK, now the statement (A or B) is true if either A is true, or B is
> true, or both. (A or B) is true for the elephant. (A or B) is true for
> the St. Bernard. That's not a problem. The claim is that
> (A xor B) => (A or B), and what that means is if I choose an X such
> that (A xor B) is true, then (A or B) is true.
>
> Symbolically, this is written with a double arrow to the right =>
> Nobody would read this as "implies all of". There's no such phrase. If
> the second statement implies the first, we can write a double arrow to
> the left <=. If both implications hold, we write a double-headed
> arrow: <=> This can be read as "the two statements are equivalent" or
> "the first statement is true if and only if the second statement is
> true". That seems to be what you think "implies" means, when you
> mutate it into "implies all of".
>
> For the elephant, (A xor B) is true. If I say that this implies (A or
> B) is true, it means the elephant satisfies (A or B). What the hell
> would it mean to say that the elephant satisfies "all of" (A or B).
>
> > anymore than his assertion
> > that sqrt(x) has only one possible answer does.
>
> sqrt(x) is the symbol which is conventionally taken to stand for the
> non-negative root when x >=0, and i times a nonnegative value when x <
> 0. It stands for only one of the two possible square roots of x. The
> reason it is useful is that it is useful to have a "square root
> function", and functions are single-valued.
>
>                   - Randy
>
Doesn't matter to me if you don't know that (-1) * (-1) = 1, Randy.
You can beleive the only root of 1 is 1 if you want to.
(chuckling)
Androcles