Doubt on Floating Point Arithematic in Lesson 1

It is discussed here that

|\epsilon| \leq \epsilon_{machine}

But, it should be other way around, i.e.

|\epsilon_{machine}| \leq \epsilon

since as \epsilon_{machine} is the smallest measurable quantity, as the gap between 2 consecutive numbers increases gradually on either sides of number line as shown in the class notebook.

Also, its discussed that

fl(x) = x . (1 + \epsilon)

But, it can be either of

fl(x) = x . (1 + \epsilon)


fl(x) = x . (1 - \epsilon)

based on which its more close to.

Any thoughts on this?