NOT.3:5.2 - Recover what an interval notation means before using it

A signal plan contains the pair (2, 4). The notation designer must say whether the second component is an ending time or a duration. Under the first interpretation, the planned active interval is [2, 4); under the second it is [2, 6). Half-open intervals include their start and exclude their end.

Choose (start, duration). Give the reader two operations: add duration to start to obtain the end, then test whether a queried time is at least the start and less than the end. At time 5 the planned signal is active, because 2 <= 5 < 6. If duration changes from 4 to 2, the new end is 4, and the signal is inactive at time 5.

The pair’s two numeric entries did not establish this interpretation by themselves. The chosen convention and the comparison procedure make the answer obtainable. A timeline can support another reading by locating the queried point against a drawn interval, provided its scale and endpoints carry the same values.

This answers a question about the plan. To determine whether a device actually emitted the signal at time 5, obtain the relevant observation and the conditions relating it to emission. The notation can retain that observation or a model of the device, but the planned interval alone supplies neither.