Yeah, that one bothered me as well, though to be fair, it is a hard condition to phrase. You also gave a definition that isn't quite right, as 2^53 + 2 is an integer value that can be represented exactly with a 64-bit float without truncation :) Perhaps you meant "exactly" in a somewhat more nuanced way.

You'd have to phrase it as something like every positive integer less than or equal to 2^53 can be exactly represented with a double precision float. Of course, there are more positive integers above 2^53 that can be exactly represented by a double than there are below, they're just spread farther and farther apart, as you said.