Now and then I see domains defined as in this example:

1) $\displaystyle x \geq \epsilon > 0$

for any epsilon greater than zero, no matter how small.

I would be tempted to believe that the above cannot be much different from

2) $\displaystyle x > 0$

as in my understanding that already excludes the case x=0.

Yet, there must be some subtle reason why some author prefers to explicitly write it as in 1)

Can it be just a matter of conventions ? or am I missing some fundamental definition ?

Thanks

Luca