[Math] Is the statement “for any real number x, abs(x − 1) = abs(x) − 1” true or false

Question

In the book, Discrete Mathematics with Applications, it says that this statement is true, however if we set x = 0,

abs(0 – 1) = abs(0) – 1
abs(-1) = 0 – 1
1 = -1

which makes me think that its false. I know books can be wrong, but I just want to make sure I didn't do something stupid.

Answer 1

If it is Ex.15, page 197 of : Susanna S.Epp, Discrete Mathematics with Applications (2010), it is not the absolute value function, but the floor function :

For all real numbers $x, \lfloor x − 1 \rfloor = \lfloor x \rfloor − 1$.