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Student Support Forum: 'Bug in Mathematica?' topicStudent Support Forum > General > "Bug in Mathematica?"

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Author Comment/Response
David
08/25/10 04:22am

Hi

Consider the following query:

Reduce[
ForAll[{A, B}, 0 <= A <= B <= 1 && 3/2 < A + B <= 2,
Abs[A1 - A] >= Abs[B1 - B] && 0 <= A1 <= B1 <= 1
], {A1, B1}, Reals
]

on which M7 yields:
(0 <= A1 < 1/2 && 1/2 (1 + 2 A1) <= B1 <= 1) || (A1 == 1/2 &&
B1 == 1) || (A1 == 1 && B1 == 1)

Now, if I only change the Abs[A1 - A] >= Abs[B1 - B] to Abs[A1 - A] > Abs[B1 - B]:
Reduce[
ForAll[{A, B}, 0 <= A <= B <= 1 && 3/2 < A + B <= 2,
Abs[A1 - A] > Abs[B1 - B] && 0 <= A1 <= B1 <= 1
], {A1, B1}, Reals
]
M7 yields:
(0 <= A1 < 1/2 && 1/2 (1 + 2 A1) <= B1 <= 1) || (A1 == 1/2 && B1 == 1)

So. My guess is should I put Abs[A1 - A] == Abs[B1 - B] I ought to get (A1 == 1 && B1 == 1).
But M7 on the following input
Reduce[
ForAll[{A, B}, 0 <= A <= B <= 1 && 3/2 < A + B <= 2,
Abs[A1 - A] == Abs[B1 - B] && 0 <= A1 <= B1 <= 1
], {A1, B1}, Reals
]

Returns False.

Am I missing smth or is there a bug?

Thanks for replies.

Best, David

(I've also attached .nb sources.)

Attachment: zanimivost-bug.nb, URL: ,
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