THis is what I am saying ..... if the clock reads 25 on the shoot clock, we don't know if that is 25.9 or 25.0. That is why you wait for the clock to read 24. Now you know for sure that 10 seconds have run off the clock. This is not that hard. Since the clock starts at 35.0 then 25.1 is not 10 seconds.

True, 25.1 is not 10 seconds, but what most people have been trying to say is that at 25.1, the clock would display 26.

Consider this. You start the clock displayed at 35. It takes a second to switch to 34, so there must have been some time elapsed before 34 seconds. Here is what the clock shows, and what the actual time could be:

35/35.0 --> 34.1
34/34.0 --> 33.1
33/33.0 --> 32.1
(etc, etc)
26/26.0 --> 25.1
25/25.0 --> 24.1
(etc, etc)
03/3.0 --> 2.1
02/2.0 --> 1.1
01/1.0 --> 0.1
00/0.0 ------------>

This is somewhat the opposite of when the game clock ticks down with tenths, and the people shout "FIVE" when the clock is really near six (5.9) and then wonder where the horn is at 0.9.

Exactly correct. This is how a shot clock works.