On 2006-01-10, Mark Calabretta wrote: > I can't let this one pass - UTC is continuous and monotonic. In fact, > ignoring differences in origin, UTC = TAI. Surprised? If so then > you're confusing a quantity with its representation (though in good > company in doing so).

I do not understand. As a function of TAI, UTC is neither continuous nor monotone increasing in the mathematical sense. In the defining document, [ITU-R TF.460-6], UTC is given as UTC = TAI - DTAI where DTAI is a step function of TAI assuming as values only integral multiples of 1 s. Unless constant, such a function is not continuous on a connected domain in the mathematical sense. Hence, UTC is not a continuous function of TAI. At some instant when TAI took a value in the positive leap second between 2006-01-01 + 00 h + 00 min + 32 s and 2006-01-01 + 00 h + 00 min + 33 s (the exact instant is not clear from [ITU-R TF.460-6 2002]), DTAI jumped from 32 s to 33 s; thus, UTC is not a monotone increasing function of TAI either. Perhaps you consider UTC as a function of something other than TAI where it may well be continuous or monotone (eg, as a function of itself, UTC trivially is both continuous and monotone). Reference: [ITU-R TF.460-6] "Recommendation ITU-R TF.460-6 Standard-frequency and time-signal emissions". 2002 Geneva. Michael Deckers