It’s everything to do with it. Read some of the other replies.

Egregious. I feel your pain.

You’re right on all three counts. It’s not always true, f(x0) has to be L, and the function has to be continuous.

There’s notation for that - (x0 - δ, x0 + δ), so you could say
f(x0 - δ, x0 + δ) ⊂ (L - ε, L + ε)

I don’t think you can use the x0 plus minus delta in the bracket (or anywhere), because then the function that’s 1 on the rationals and 0 on the irrationals is continuous, because no matter what positive number epsilon is, you can pick delta=7 and x0 plus minus delta is exactly as rational as x0 is so the distance to L is zero, so under epsilon.

You have to say that
whenever |x - 0x|<delta,
|f(x) - L|<epsilon.

But I think this is one of my favourite memes.

Despite the fixes, theft claims for the affected Hyundai and Kia models continue to exceed industry norms, including for vehicles equipped with the upgraded software, according to HLDI. One reason could be that the software-based immobilizer only activates if the driver remembers to lock the vehicle with a fob, while many people are in the habit of using the switch on the door handle.

If ever there were a problem that is ripe for fixing with the first version of the software upgrade, not a future one, this was it.

We’ve all had nights like that.