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From: Michael Deckers <Michael.Deckers_at_fujitsu-siemens.com>

Date: Wed, 11 Jan 2006 10:47:25 +0000

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
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*> 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

Received on Wed Jan 11 2006 - 02:47:56 PST

Date: Wed, 11 Jan 2006 10:47:25 +0000

On 2006-01-10, Mark Calabretta wrote:

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

Received on Wed Jan 11 2006 - 02:47:56 PST

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