Propositional functions: P(8) where P(x): x > x - 1 is false?

[sacred horizon]

I'm not sure if this is a teacher's mistake, but it says that P(8) where P(x): x > x - 1 is false but wouldn't this be true? --> P(8): 8 > 8 - 1 = 8 > 7?

EDIT 1: Could it be that it is missing the part where we describe what x is thus making it false?

EDIT 2: Oo would this have to do with specifying the universe or domain of discourse or the existential quantifier?

[worn torrent]

...I mean, it's true for all real x.

And it's not defined for complex x.