Contradiction in an absolute value property?

[Hacca]

An absolute value property is
$$\lvert a \rvert \geq b \iff a\leq-b \quad \text{ or } \quad a\geq b,$$ for ##b>0##.

Is this true for the case ##a=0##?
I mean if ##a=0, \lvert a \rvert =0## so ##0 \geq b##. But ##b## is supposed to be ##b>0##, so we have a contradiction.

How can this property be true if ##a=0## is false?

 

[BvU]

It's not the property you are 'testing', but the statement . The statement holds.

 

[mfb]

For a=0, b>0, both sides of the equivalence are false. The equivalence itself is correct.