I didn&#x27;t say they were <i>intervals</i> (I&#x27;m well aware of interval representations for numbers, which single point rationals are not).<p>&gt; <i>that floating point numbers by definition form an exact rational subset of the extended real line.</i><p>Sure, that&#x27;s what they <i>form</i>; it&#x27;s not what they (usually) <i>denote</i>.<p>&gt; <i>It&#x27;s also false that the floating point number _f_ is the midpoint of the set of numbers that round to _f_;</i><p>It is close enough to being the case for my purpose in the grandparent article. Whether the cluster of numbers is lopsided one way or the other doesn&#x27;t really detract from my point.