[A lot of discussion on this list seem to revolve around people understanding terms in different ways. In an impractical example of that spirit...]
> I do not understand. As a function of TAI, UTC is neither continuous > nor monotone increasing in the mathematical sense. To say if TAI is a monotone function of UTC, you need to put an order on the set of possible TAI and UTC values. To say if UTC is a continious function of TAI, you need to put a topology on both. To me, TAI seems to be a union of copies of [0,1) labelled by YEAR-MM-DD HH:MM:SS where you glue the ends together in the obvious way and SS runs from 00-59. You then put the obvious order on it that makes it look like the real numbers. OTOH, UTC seems to be a union of copies of [0,1) labelled by YEAR-MM-DD HH:MM:SS where SS runs from 00-60. You glue both the end of second 59 and 60 to the start of the next minute, in adition to the obvious glueing. I haven't checked all the details, but seems to me that you can put a reasonable topology and order on the set of UTC values that will make UTC a continious monotone function of TAI. The topology is unlikely to be Hausdorf, but you can't have everything. > DTAI jumped > from 32 s to 33 s; thus, UTC is not a monotone increasing function of > TAI either. Since DTAI involves subtracting quantities that aren't real numbers, you can't conclude that a discontinuity in DTAI results in a discontinuity in UTC. David.