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I'm pretty sure that the following is true, but I don't see an immediate compelling proof, so I'm going to throw it out as a challenge:
Let [itex]A,A', B, B'[/itex] be four real numbers, each in the range [itex][0,1][/itex]. Show that:
[itex]AB + AB' + A'B \leq A' B' + A + B[/itex]
(or show a counter-example, if it's not true)
This inequality was inspired by Bell's Theorem, but that's not relevant to proving or disproving it.
Let [itex]A,A', B, B'[/itex] be four real numbers, each in the range [itex][0,1][/itex]. Show that:
[itex]AB + AB' + A'B \leq A' B' + A + B[/itex]
(or show a counter-example, if it's not true)
This inequality was inspired by Bell's Theorem, but that's not relevant to proving or disproving it.