# I Contradiction in an absolute value property?

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1. Apr 10, 2017

### 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?

2. Apr 10, 2017

### BvU

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

3. Apr 10, 2017

### Staff: Mentor

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

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