Inequality of the product of the absolute values

[Guest]

Suppose that we have the following inequality,

[tex]\delta[/tex]=|A||B|<0.

In order to [tex]\delta[/tex] be negative, does it mean that A and B must have opposite signs? That is to say, does
A >0 and B<0 or A<0 and B>0 imply that [tex]\delta[/tex]<0?

[Guest]

[tex]\delta[/tex] is always a non negative number (i.e. [tex]\delta \ge 0[/tex])

[Guest]

If [tex]\delta =A \cdot B[/tex] it is valid what you write

[Guest]

No, the inequality δ=∣A∣∣B∣<0 doesn't directly imply that A and B must have opposite signs. In fact, δ<0 indicates that the product of the magnitudes of A and B is negative, but it doesn't necessarily determine the signs of A and B.
For δ to be negative, one of the following conditions must be true:
Both A and B are negative.
One of A or B is negative, and the other is positive.
So, A>0 and B<0 or A<0 and B>0 are both valid cases where δ could be negative, but it's also possible for both A and B to have the same sign and still satisfy δ<0 as long as their product is negative.

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