The hour that never happens

Once a year, in spring, the clocks jump from two o'clock straight to three. The hour between them never happens.

Once a year, in spring, the clocks jump $2:00\to 3:00$. The hour between them never happens.

hour between $h$: $2:00\to 3:00\Rightarrow \nexists h$.

If you sleep from eleven at night to seven in the morning, you usually sleep eight hours. On that night you sleep only seven, because one hour was skipped.

Sleep from $23:00$ to $7:00$ is usually $8$ h. That night it is $8-1=7$ h, because $1$ h was skipped.

$23:00\to 7:00$: $8-1=7$.

The lesson: if you want eight hours that night, go to bed at ten. By real time you sleep from ten until six, which is eight hours, and the clock in the morning says seven. Count the hours you sleep, not the numbers on the clock.

Lesson: for $8$ h that night, go to bed at $22:00$. In real time $22:00\to 6:00$ is $6+24-22=8$ h, but the morning clock shows $6+1=7$. Rule: sleep $\Delta t\ge 8$ h, whatever the clock says.

$22:00\to 6:00$: $6+24-22=8$; clock: $6+1=7$. Rule: $\Delta t\ge 8$.

In autumn the clocks go back from two to one, and the night is nine hours long. Over the year the hour that was taken is given back, so nothing was stolen, only borrowed.

In autumn the clocks go back $2:00\to 1:00$ and the night is $8+1=9$ h. Over the year $-1+1=0$: nothing stolen, only borrowed.

$2:00\to 1:00$: $8+1=9$. Year: $-1+1=0$.