Yes. But in order to understand limits, you must think in ranges and not on the reaching point. You don't divide by zero, you measure everything until 0, but 0 itself is not measured.

BTW, 5.000000000000000..1 - 4.999999999... > 0

>You can't divide a number in half

Declare any number which can't be neither higher or lower than it's half.

> “he is on the side of those of us who think that physics doesn’t accord with our experience and therefore it’s missing something.”

It seems more likely that we don’t understand how our experience works as well as some of us think we do. In other words, the mismatch is more on the side of the experience than of physics.